Will Mass Effect 2 bought in US work in UK?
Solution 1:
For a PC, there should be no issue as Eric states. For consoles, there may not be an issue, and it all depends on a lot of factors.
Games are never format dependent, though they may be region locked. It's purely a limitation that's there because the manufacturer wanted it to be; once that has been bypassed one way or another (modding, FreeLoader, Action Replay...), then it can become possible to run the game.
IIRC, the only connection method that may cause problems is using an RF adapter; none of the others are subject to issues because they don't use PAL/NTSC/NTSC-J for transmitting the signal. All consoles these days support a 60Hz output, and I can't remember the last time I saw a TV that didn't support 60Hz input. (I'm not entirely sure about how it looks for US/Japan for TVs that can do 50Hz, but at least for modern consoles, all games can run in 60Hz anyway.)
Additionally, the PS3 is advertised as being completely free of region locking for PS3 games, while for the XBox 360, some games are actually region-free, and Mass Effect 2 is supposedly one of them.
So no, you should have no problem at all, regardless of which system the game is for - as long as your console works with the TV (which it should, although you may need a power adapter if your console is not bought locally).
Solution 2:
The answer depends on your platform. PC games should work worldwide without any problems.
Console games however are format dependent. The main formats are NTSC, NTSJ and PAL. NTSC is used (mostly) in America and UK uses PAL format (usually). NTSJ is a special japanese format that will prevent you from compatibility with the rest of the world.
The main difference is about TV standards across the world which are slightly different from one country to another, so the console has to adapt and therefor, the games have to adapt to the different consoles.
Refer to this map for general format compatibility