Being based in the UK myself, I would say that most people probably don’t click the “Sites from the UK button.”
One thing that I have noticed is that if you search any of the Google sites it tries to tailor the results from the country in which the search has been performed. At work, my machine is linked to a server in the US, and doing a search in Google.com, gives slightly different results than the same search at home.
I’ve also heard that Google would give a domain, say, http://www.xyz.com, on a UK server more precedence than the same domain on a US based server if the search was done from the UK and vice-versa.