I am a counsellor. My wordpress blog is mylocation counsellingandsupervision.co.uk. If I google, bing, yahoo my name my site comes up 1st or 2nd. If I google, bing, yahoo "mylocation counselling supervision" in any combination the search engine does not find anything. If I have uploaded all the usual plugins etc I would like to know how search engines pick up my name but not the words of my website address.
Search engines use a number of factors when putting your website in search results, not just the name of the site. The reason you score highly for your name but not your location is probably because in the words in and around the links to your site your name and not your location is used.
For such a specific research as being found when you type in Google “location Counselling Supervision” (maybe also with quotes) it should suffice changing the code you find in tag of your blog's pages.
Now in the title you have this mess:
You can see it shows up in the title bar of the browser window, you should substitute it with this:
The trick should be enough. Otherwise try adding the same text as text at the top of your pages.
After the change you need to wait, in worst cases even 30/90 days for Google to update its index.
As a side note I would strongly advise you to hire someone who can fix your blog. Even the meta description and the text itself in the top of the pages is all wrong.
One reason (besides the title issue already noted by Marco Demaio) why your site may be scoring so badly on Google is that you have very little actual content on it. Almost all of your pages are identical copies of the same feedback form — about the only ones that have any non-trivial content at all are the main page and the "Latest News" page (which has your new year's greetings test post on it).
(Indeed, that page does come up for me, on page 13, when Googling for North London Counselling Supervision. Of course, this question comes up on page 4, so I would indeed say that you have an SEO problem.)
My suggestion would be simply to write up some useful content on all your pages and wait for Google to reindex them. If you can't think of anything relevant to write on some page, consider whether you really should have that page at all.