The kndle can connect in two ways...
Wireless, which uses a normal Internet connection like you'd have in your home and use with a laptop or it can also be used by joining any free wireless hotspot. This way will work in any country as long as you are near a wireless access point you can use.
3G, this uses a mobile phone network and requires a sim card in the kindle (just like the one in any mobile phone) this method will only work if you have the correct sim card for your country in the kindle. so a USA kindle would not have the ability to connect to the UK mobile phone network.
Also you would have to pay import duty on the kindle if you bought it abroad and tried to bring it into this country.