'What I have written' 
Good luck!
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Apart from that, I can't see a single earth shattering problem that is causing your site to drop just a lot of things wrong with the site which combined, may be causing that effect.
I have scanned the site and:
1. Duplicate content 911 pages but most are 'order' pages and those related to Trip Advisor - they don't seem to be doing you any harm as most of the searches are high up, eg dog friendly B&B in Paignton
These pages are dominated by a huge hero graphic that takes the whole of the top of the page then a search box - I would consider removing the graphics and starting these pages at the listings. I would then add some descriptive content surrounding the themes.
I would check in Google - GSC how the site handles the 'order' parameter - as it narrows/sorts content - maybe adjust the setting to that.
You have a lot of listings which are incomplete - I'd remove the wording Awaiting Copy as it's on all of these:
https://www.englishriviera.co.uk/accommodation/green-gables-brixham-p2165183
https://www.englishriviera.co.uk/accommodation/rose-cottage-torquay-p2164293
https://www.englishriviera.co.uk/accommodation/22-rowley-road-torquay-p2165423
https://www.englishriviera.co.uk/accommodation/29-north-furzeham-road-brixham-p2165243
https://www.englishriviera.co.uk/accommodation/53-north-view-road-brixham-p2165543
https://www.englishriviera.co.uk/accommodation/3-curlew-brixham-p2165663
https://www.englishriviera.co.uk/accommodation/3-plover-brixham-p2165693
https://www.englishriviera.co.uk/accommodation/1-mount-ararat-brixham-p2165483
https://www.englishriviera.co.uk/accommodation/5-manor-court-brixham-p2165033
https://www.englishriviera.co.uk/accommodation/19-prospect-road-brixham-p2164913
https://www.englishriviera.co.uk/accommodation/34-mount-pleasant-road-brixham-p2165353
https://www.englishriviera.co.uk/accommodation/1-elkins-hill-brixham-p2165343
https://www.englishriviera.co.uk/accommodation/53-king-street-brixham-p2165493
https://www.englishriviera.co.uk/accommodation/148-preston-down-road-paignton-p2165533
https://www.englishriviera.co.uk/accommodation/28-kelland-close-paignton-p2165553
https://www.englishriviera.co.uk/accommodation/125-reddenhill-road-torquay-p2165103
https://www.englishriviera.co.uk/accommodation/8-heath-rise-brixham-p2165513
https://www.englishriviera.co.uk/accommodation/3-4-coastguard-cottages-torquay-p2164143
https://www.englishriviera.co.uk/accommodation/the-midland-hotel-paignton-p2163533
https://www.englishriviera.co.uk/accommodation/4-dunlin-brixham-p2165673
https://www.englishriviera.co.uk/accommodation/20-devoncourt-p2164493
https://www.englishriviera.co.uk/accommodation/1-heath-court-brixham-p69543
https://www.englishriviera.co.uk/accommodation/5-warefield-road-currently-closed-p2162553
https://www.englishriviera.co.uk/accommodation/beach-cottage-torquay-p2164303
https://www.englishriviera.co.uk/accommodation/parkholm-hotel-paignton-p2162223
https://www.englishriviera.co.uk/things-to-do/regency-palace-arcade-paignton-p2108783
https://www.englishriviera.co.uk/accommodation/21-prospect-road-brixham-p2165443
https://www.englishriviera.co.uk/accommodation/linden-house-torquay-p52503
https://www.englishriviera.co.uk/accommodation/brackencroft-guest-house-paignton-p2162253
https://www.englishriviera.co.uk/accommodation/wassail-cottage-paignton-p2165573
https://www.englishriviera.co.uk/accommodation/1-3-6-and-4-barn-road-paignton-p2164163
https://www.englishriviera.co.uk/accommodation/4-marine-parade-paignton-p2165793
https://www.englishriviera.co.uk/accommodation/4-clifton-grove-paignton-p2164463
https://www.englishriviera.co.uk/accommodation/bridge-cottage-paignton-p2165563
https://www.englishriviera.co.uk/accommodation/8-torwood-gables-torquay-p557253
https://www.englishriviera.co.uk/things-to-do/the-match-room-sports-and-social-club-p2161733
https://www.englishriviera.co.uk/accommodation/riviera-nights-guest-house-torquay-p2162103
https://www.englishriviera.co.uk/accommodation/59-rock-road-torquay-p2165083
https://www.englishriviera.co.uk/accommodation/6-manor-house-torquay-p757773
https://www.englishriviera.co.uk/accommodation/chestnut-lodge-torquay-p77403
https://www.englishriviera.co.uk/accommodation/6-lisburne-place-torquay-p2164223
https://www.englishriviera.co.uk/accommodation/5-hesketh-mews-torquay-p92523
https://www.englishriviera.co.uk/food-and-drink/jia-wang-chinese-takeaway-torquay-p2164213
https://www.englishriviera.co.uk/accommodation/the-dorchester-torquay-p2165283
https://www.englishriviera.co.uk/accommodation/springfield-torquay-p2163753
https://www.englishriviera.co.uk/accommodation/34-braddons-hill-road-east-torquay-p2165293
https://www.englishriviera.co.uk/accommodation/15-broadstone-park-road-torquay-p2165063
https://www.englishriviera.co.uk/things-to-do/park-lane-torquay-p2374483
https://www.englishriviera.co.uk/accommodation/oddicombe-hall-hotel-torquay-p2163003
https://www.englishriviera.co.uk/accommodation/chelston-mount-torquay-p2162053
https://www.englishriviera.co.uk/accommodation/danecroft-brixham-p2165143
https://www.englishriviera.co.uk/accommodation/17-north-furzeham-road-brixham-p2165203
https://www.englishriviera.co.uk/accommodation/mandalay-apartments-paignton-p1530123
https://www.englishriviera.co.uk/accommodation/nevada-holiday-flat-lets-paignton-p2164173
https://www.englishriviera.co.uk/things-to-do/go-karts-at-quay-west-paignton-p2160333
https://www.englishriviera.co.uk/accommodation/16-braddons-hill-road-east-torquay-p2164253
https://www.englishriviera.co.uk/food-and-drink/broadsands-beach-cafe-paignton-p2106033
Duplicate Description & Titles: You have quite a lot - some are from the sort/order others need separating out:
All of these have the same Description: 'you’ll find plenty of dog-friendly hotels and holiday accommodation here on the English Riviera, Devon’s Beautiful Bay'
With this title: 'Dog Friendly Hotels in Torbay, Pet Friendly Hotels - English Riviera'
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=alphaDesc
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=alphaDesc
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=alpha
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=alpha
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=tripadvisorratingDesc
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=guidepriceDesc
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=guideprice
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=guidepriceDesc
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=guidepriceDesc
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=alphaDesc
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=tripadvisorratingDesc
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=grading
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=alpha
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=guideprice
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-brixham?order=grading
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=guideprice
https://www.englishriviera.co.uk/accommodation/by-location/dog-friendly-accommodation-torquay?order=grading
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation?order=tripadvisorratingDesc
https://www.englishriviera.co.uk/accommodation/by-location/babbacombe-dog-friendly-accommodation
Awaiting Further Details - duplication
https://www.englishriviera.co.uk/whats-on/babbacombe-model-village-easter-egg-trail-p1413873
https://www.englishriviera.co.uk/whats-on/super-summer-trail-bygones-p1491443
https://www.englishriviera.co.uk/whats-on/half-term-coin-mystery-bygones-p1826943
https://www.englishriviera.co.uk/whats-on/half-term-teddy-bear-picnic-bygones-p1491313
https://www.englishriviera.co.uk/whats-on/easter-holidays-egg-hunt-bygones-p1666163
https://www.englishriviera.co.uk/whats-on/halloween-hunt-bygones-p1449143
Finally, a lot of descriptions are too long - over 156 characters.(1252 including order pages)
A lot of titles too long - (474 including order pages)
You have no canonicalisation at all and best practice is to self-canonicalise.
Apart from that?
Little written content.
I'm guessing that a lot of this would have been on the previous site anyway - the overuse of large hero graphics is an irritation as you have to scroll to see content. There is no simple search - it's complicated and seems to appear on every page.
Missing
No Twitter cards
No Facebook OG
No Schema.org
So lots missing but nothing that a good SEO couldn't sort for you.
It is a combination of lots of things.
I hope this helps.
Regards
Nigel
I think you are now at risk of overthinking everything.
Use the MOZ list I gave you and write a page.Then let me see it. - I feel I've written it already lol! 
Use the core Keyphrase as Piedmont Bike Tours and write some interesting content on the subject.
Don't have a fixed number of semantics, write freely, when you think you are about to repeat yourself use a synonym or semantically connected phrase.
If you carry on as you are you'll never write anything, and will become bogged down in Rankbrain, Proxemics and Semiotics!
It's time for action - (Don't look up those words as you will end up in a rabbit hole screaming to be let out!)
Regards
Nigel
Hi SDavis11
The main point here is that each page should focus on a particular theme or subject, If you start overlapping then you will dilute any link juice between pages. Taking your points one by one:
1. If you have an article which is unrelated to your website topic then consider noindexing - or just leaving it alone. If you 301 to the main site then you are telling Google that the page has moved and that the main site is the new version. It is not. Any backlinks you do have are linking to that page because they feel that it is relevant to them. If they are suddenly linking back to the home page which is not relevant you end up:
a. Upsetting those who link to you as they are not now connected to relevant content.
b. Having a toxic backlink to your home page from non-relevant content.
2. If the article (I assume this in ON your site and not _TO) _has more irrelevant content - first I would question why you keep producing irrelevant articles then I would remove any site related keywords. Then treat it like point 2. Retitle it and let it breathe on its own. this will benefit the article and the site as you have removed overlapping themes from the title.
3. If you have a relevant topic in an article on the site then beef it up. If it's a 300-word article and it's ranking reasonably well then it is likely that the content is not enough to fully satisfy a user's query and that is why the engagement is low.. Extend the article, serve the answers as quickly as you can, above the fold and internally link to pages that will lead to a conversion.
Write semantically connected and strong content written around your theme which invariably will be a medium to long length keyword or phrase. Make the writing rich without overstuffing.
I hope that helps
Regards
Nigel
Hi seoanalytics
As you have already pointed out each page has a 'theme'
We have established that the theme is the most important Key Phrase on the page. ie Piedmont Bike Tours.
You do not _have _to search for every semantically connected word or phrase and use them all because Google understands what the theme is. You merely need to support the theme with some semantically related content that can contain some supporting baby anchor words and phrases spun within the writing ina contextually relevant way
You need to write from scratch with this in mind.
If you just plop some words and phrases in it will not read correctly.
Rankbrain, which is Google's new(ish) way of ranking pages using AI, understands what a theme is - you are merely helping it understand.
You risk keyword stuffing with the approach you suggest.
Regards
Nigel
Hi Andrew
If you go to the search results from the INURL link I put there then go to the right of the URL there is a green arrow. Hit that and the word 'cached' and you will see a version of the page as scraped by Google with a caching date.
Regards
Nigel
Only because you mentioned it further up - I was looking for synonyms for the word 'region' - you don't need it really. Although I suppose you could include a map with the trails picked out in red?
Regards
Nigel
I think it's better to use your brain for this and Google - you just don't need to be so rigorous about it. Google isn't necessarily looking for synonyms and semantics - it's only if those terms are being searched and form part of the family of words and phrases surrounding the main term.
If there are none, there are none.
However I have attached a MOZ download of Alsace Region and Alacse Bike Tours - this gives you an idea of what MOZ is showing for related searches but frankly they are the same as if you had done this yourself in the search box. e.g. alsace cycling holidays, guided cycling tours france, cycling alsace self guided.
The point is you don't need all of them in order like some list. You need to write properly constructed sentences where you can 'pepper' the text with some of them.
Regards
Nigel
Exactly!
Yes the Topic will be 'Alsace Bike Tours'
You will start the piece with:
The Alsace region is in the northeast of France bordering Germany...
Then go on to describe it in a little detail - is it mountainous, very flat, hills, mud tarmac/concrete ...etc...)
Then describe the tours themselves in greater detail.
I think routes, tours and trails fall very close to each other - all three are semantically related if not close synonyms! 
Regards
Nigel
Hi Andrew
If you type in to Google - site:https://www.englishriviera.co.uk inurl:http:
You will see that there are around 255 http pages still indexed some of which were cached on the 19 December so I am guessing that your switch from HTTPS was quite recent.
While Google resolves these pages there can be an overlap with both versions ranking and of course, Google sees them as duplicates. It is fairly common to see a short drop in rankings because of this but it is not permanent. Google favours HTTPS sites over standard HTTP so it should not be long it comes bouncing back.
I would go through the URLs you find by that search (above) and check that they all redirect. Meanwhile more on the switch here:
https://security.googleblog.com/2016/09/moving-towards-more-secure-web.html
and: https://support.google.com/webmasters/answer/6073543
There is also a helpful checklist here: http://searchengineland.com/http-https-seos-guide-securing-website-246940
Regards
Nigel
Hi seoanalytics
These are words which have a similar meaning or when they are commonly used interchangeably by searchers. So, in essence, yes, both synonyms and semantics!
You're getting there! 
Regards
Nigel
Hi seoanalytics
Lexical semantics and synonyms are similar in that, whilst a synonym is one word which can be substituted for another - Bike / Bicycle - Lexical semantics deals with the meaning of the word or phrase.
A bike or a bicycle is a machine for conveying a person from one destination to another. The meaning of the word is that it is a self-propelled mode of transport. A synonym of a bike is simply 'a bicycle' - no need for any explanation.
LSI or latent semantic indexing is an old acronym that really shouldn't be used in relation to modern semantics. It was originally used in the 80's as a way of indexing complex information. A form of data retrieval - most high-level SEOs completely poo poo its use these days so it's best to ignore LSIs and focus on the concept of semantics in its true sense.
I think the danger here is that you risk getting bogged down in the subject and over optimising your page. The essence of great writing can be lost in a desire to fill the page with every conceivable permutation of synonym and lexically connected words and phrases. In doing so you risk either over stuffing or getting it wrong. Worse still, spending just too much damn time on it!
The topic is the place to start as that is the highest level. So the topic, for example, is Bike Tours In Piedmont.
Synonyms can simply include the words Bicycle as opposed to Bike and for example Routes and Trails.
Semantics are the wider meaning - so 'Biking through Italy'
In my reply on Dec 22 I said that you must focus on 'what people might type in' and what you are seeing in the Google suggestion tool and the related searches at the bottom are firstly the most common words and phrases typed in and secondly what Google believes are closely related searches.
Like I have said all along - don't get too bogged down in this - the knowledge you have learned here is likely to be 100 times better than any other site competing with you - trust me! No one I have ever helped has gone into this subject as deeply as you! So you will be miles ahead!
Related topics are separate pages - don't mix them up. It's very much in the writing of the sentences so when I use the word 'pepper' this means intertwining or 'sprinkling' it into your content.
Finally, if someone bangs on about LSIs then ignore them as they do not know what they are talking about. Too little knowledge is a dangerous thing.
Regards
Nigel
Hi seoanalytics
Most people don't bother with the plural problem but I always use plurals when I think the customer will type that in preference to the singular. Seach results always differ (just type in 'bike') so it is important.
For me, Piedmont Bike Tours wins every time because that is what people will type in - regardless of the fact you only have one.
How many times? - once! - you will have an H1 which will say it and close semantics, so 'trail biking' etc so don't overdo it - even if you are writing 1000 words I would still only say that max, twice. Then let the baby anchors do their work.
Best of luck. If your site is updated then you will see an improvement right quickly - in my experience, you will see a bump then a drop back so don't be alarmed when this happend.
Cheers - have a great holiday! I'm off to the pub 
Nigel
It depends on a lot of factors - the most relevant one is the frequency of site crawl. Some pages can take 6 weeks - search for the page in Google and hit the down arrow to check the last time it was cached.
Fetch Google in search console as this can speed things up.
If it's a brand new site it can take a while!
You're selling Bike Tours in Piedmont and whilst it is no problem mentioning related topics the more you write about related items and less about the core topic the more you dilute your page.
The more people you listen to with conflicting/nuanced views, the more stressful and ultimately impossible it is to finish the job in hand.
Write the page - watch the ranking - adjust as necessary!
You aren't going to be criticised as you have taken great advice and you are going to write a top ranking page.
Frankly I would stick to Piedmont Bike Tours. It's no problem mentioning Barolo and Barbaresco in the text but once you start adding headings you are diluting the thrust of the page.
LSI keywords are a bit if misnomer but loosely they are semantically connected words and phrases - similar are produced by MOZ with monthly search volumes. There is a free tool that just spits them out. I think you have more than enough sources for these as you are in the industry - just don't think you need to stuff them all in. Remain focused.
You need to think about words like 'best' 'easiest' 'scenic' and other terms people may type in.
Regards
Nigel
Yes but not too wide related topics. If it's too far away then make a separate page!
You need one image named with the focus keyword - 'Piedmont Bike Tours' so instead of saving it as eg DSC168541 - straight from the camera, name the image 'piedmont bike tours' so its URL will be site.com/piedmont-bike-tours.jpg. Make sure it is no bigger than say, 75k to keep page speed up.
Then make the alt tag of the image 'Piedmont Bike Tours'
Other images must be named in this way.
the alt is like this

Keep the alts short & descriptive.
eg 'Barolo Wine'
etc
Regards
Nigel
H1's are not for sentences, they are punchy headers incorporating the main keyword, designed to catch the eye.
H2 - yes exactly
Barolo Wines - Exactly right.
Get some images, named as the subject with alt tags in there as well.
Regards
Nigel
OK 
Yes, keep it fluid, there is no need to group them together. Make it read naturally.
The best way to format the Meta title tag is like this
'Main Keyword - Related Keyword (or higher category) - Company Name' so
'Piedmont Bike Tours - Cycling in Italy - Company Name' (keep under 60 characters)
Meta description: Make this your call to action - it does not help SEO per se so don't fill it with keywords.
'Book a thrilling bike tour of Piedmont in the sunny hills of Northern Italy - unbeatable prices from company name - call us on 12345678 or book online here!'
Keep it under 140 characters or Google will add an ellipsis at the end ' ...'
The H1 does not help SEO on its own, only part of the keyword density on the page. It should sit at the top of the page and contain the keyword:
The H2 does not help SEO per se but is useful for breaking up the content on the page. It is usually only used to divide content - so if you do use it make sure that you follow it with a few paragraphs. Some people advocate a minimum of 300 but it, not the number, rather the way it's written. Don't overdo the keyword, think semantically.
eg:
Keep it natural - I can't advocate that enough.
Regards
Nigel
PS when I say 'per se' I mean 'directly' - of course, a well-written description with strong headings will cause people to visit the pages and take action - the interaction through lower bounce rate and less pogo-sticking is good for SEO, obviously.
Semantic similarity is the most important thing and that comes from you, the writer and the tools you use to provide contextually similar words. Clearly, 'bike' and 'bicycle' are almost semantically identical and can both be used on the page as variants. The closer the keywords are together the more targetted the focus of the page but just be careful not to stuff it - remember to concentrate on writing fluidly.
You can always check a page for its relevance to a particular keyword/phrase in MOZ.
Regards
Nigel