Hi there! Thanks for providing example links and answering my questions. Those were very helpful!
I had a peek at your site, and noticed that it has several issues hindering its performance in the search results, including two major ones: 1) widespread duplicate content issues; and 2) very few inbound links. Before you do anything, though, I recommend thoroughly studying Moz's guide to SEO for beginners at https://moz.com/beginners-guide-to-seo.
Next, tackle your duplicate content issues. While you could try to sort this issue out using canonical tags (and those are almost always a good idea to use anyways - see https://moz.com/learn/seo/canonicalization for details of implementation), I would focus the bulk of your resources on planning and creating unique, highly valuable content for each page of your website. It looks like a lot of the content for each region and specialist is identical, with some of it near-identical (with the latter having simply the specialist and/or regional names updated from one page to the other only to distinguish it). This strategy is commonly used to create content on large websites that target many different regions, as it makes it easier to scale content creation, and it used to work to a certain extent to help geotargeted landing pages rank in the SERPs... many years ago. To get some ideas for creating a strategy that will work for your particular website and its audience (and please the search engines), I recommend you check out this Whiteboard Friday on scaling content for geo-targeted landing pages - https://moz.com/blog/scaling-geo-targeted-local-landing-pages-that-really-rank-and-convert-whiteboard-friday.
Now, what about those links? How do you acquire those? Once you have created the content that the audience you are targeting craves, linkbuilding will be much, much easier, as people are more apt to link to it -- without being asked. The key to making this work is to get said content in front of the right people. That is, you need to figure out how to best share and promote your content to the people you want to link to it. For more on this, I recommend studying Paddy Moogan's excellent guide to linkbuilding, which you can find at https://moz.com/beginners-guide-to-link-building.
I hope that helps! Please let me know if you need additional clarification. 
Christy
