How does google determine which sites are international and which are from the UK. Does it go by server IP?
that could depend on you are using google.com or google.co.uk google.co.uk can be very sensitive with the keyword "uk" in your domain name I doubt .... do most of the people in UK are using google.co.uk ?
A lot has to do with the content in the site, like the apperance of £ signs and locations, also the sites that link to them, if there are many .co.uk sites pointing to the site, google will also look at the content on those sites to determin the region. There are many more factors involved, even on the whois domain data if the registered owner is located in the UK.
Despite Google's addition to the Webmaster Tools, their overall methods of assigning geo-location remains unchanged. The major search engines use two common criteria to determine geo-location: (1) the presence of a Country Code Top Level Domain Name ('ccTLD' as in 'somesite.co.uk'), or (2) for generic Top Level Domains (.com, .net, .org, .info, .biz, etc.) they rely on the IP address of the server that hosts the site. Google will also sometimes look at the domain name registration data, although they don't specify how or when. Since all of the major search engines give a great deal of weight to geo-location - even when the user does not request a country-specific search - it is important to get your site's geo-location set properly. No amount of links, <meta> tags, or ritual sacrifices will have any effect on your geo-location setting. So, if you have a generic TLD, you need to have your site hosted on a server that's physically located in the target country. UK users should note that at least one well-known hosting service actually has their servers located in The Netherlands, so be sure to check this out before buying. If you have a Country Code Top Level Domain Name, then it doesn't matter where your host is located.
I'm UK here but tend to use .com for all searches unless I'm looking for products. In the webmaster world you have to think worldwide not just the UK unless it's a UK product selling site etc.