"Most" 360 games are region free which means the vast majority from the US can be played on a UK machine, or vice versa.
www.gamehubs.com is an import site if you want to check it out, it gives all region info for each game if you have any doubts and their prices are reasonable.
The only downside with some titles is that the downloadable content can be region coded, although that is more prevalent on the PS3. (ie. if you have a US disc and you want a download add-on or update from the UK site it wont work with it).
Aside from that there are no other issues I can think of.
Hope that helps somewhat,
Shugga's DH, as its easier to type it than recite it.