An American Wii will not accept European games to play due to Nintendo region locking the console. Therefore you would need to buy all your Wii games from America.
Also, if you were to buy an American Wii, for it to operate properly in the UK you would have to do a few things:
1) Quite obvious this one, but you would need an adaptor for the plug as our plugs are of a much different shape and our plugs have a lot higher voltage, so you would need to get a step-down convertor to make sure you didn;t blow the Wii up.
2) You would need a box that changed the signal from NTSC to PAL. These can be found quite cheaply all over the internet (especially eBay) and they'e generally of a good price.
Once you've done those two things (and bought American games) you would be able to play your American Wii like you would play a British one.