Hi google.co.uk allows for users to search for "pages from the UK" only How does google decide if a site is in the UK (Or, to be more specific, if I move my existing websites (.coms) to godaddy hosting, will I no longer appear in the UK search results?)
It may have an impact - it depends on what the strongest indicators are now that are telling Google where you are targeting. The best way to let google know where your intended visitors are is to set the geo targeting in Google Webmaster Tools. Other than that Google uses the tld, location of the hosting, and the geo-targeting of the sites you have backlinks from.
Google uses 4 criteria to decide the UKness of your web site/page The domain name: is it co.uk ? Server location: is the server physically located in the UK? Are the incoming links from UK websites. If you don't have a co.uk domain you can go on to webmaster tools and tell Google that it's a UK targeted site. Google may or may not believe you.
And you can always use Google Webmasters Tools to instruct the search engine to consider your website(s) aimed at a specific country, that certainly helps, too.
It works on the basis of several factors the domain name The server your using links back to you website but in reality many .com are owned by UK companies anyway, as its considered the top domain to have, because people tend to remember .com rather than anything else