Hi again Coral. There is a communication gap happening hear around a few certain words. Just fixing that will help you a lot in moving forward. Here it is...
Panda is not the same as Penguin......Panda is not the same as Penguin.....
Panda is a manual action, where you get de-indexed, get a notice, and have to do the whole terrible link removal and re-consideration request nightmare. You do not have this problem. So forget all about massive link removals and re-consideration requests.
From what you describe, you have a Penguin problem. That's just Google's programming noticing some weirdness in your link profile and either not counting the funky links or giving you a slap, a penalty, relating to those funky links (as in too high a % of a certain anchor text = a slap for your ranking for that anchor text keyword).
There are no re-consideration requests accepted for a Penguin penalty. All you can do is fix the links. And there are just a few ways to do that. Here are the ones I know of:
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if the page the funky backlinks all point to is a sub-page, and there are few good links pointing to it, you can just abandon that original page (make it a 404) and create a new page to replace it. This rarely works because usually the funky links are pointing to the homepage and you can't abandon that.
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get the links removed. If they come from a site you have some control or influence over, this is nice. But usually they are junk automated sites and there is almost zero chance of having the links removed
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Disavow the domains that the funky links are coming from. Disavowing domains is usually better that individual URLs. Especially to get rid of sitewide links. You can use it to thin out your number of links using the exact anchor text you are getting slapped for. And to get rid of links from nasty toxic malware and porn sites.
Google gave us the Disavow option for this purpose. It can be used wrong, but most tools can. A good SEO group can check out your history and link profile and tell where the problem lies. I would suggest that it is not critical that the SEO company be UK based, but it is critical that they be good and that they are willing to work with small businesses affordably. It does matter that they speak english, so UK, Canada, US, New Zealand, or Australia are all fine.