There is no such thing as a "British accent". For the love of God would people stop saying crap like that?! First of all "Britain" is three (Northern Ireland is part of the "United Kingdom" but not Britain) separate countries (England, Wales and Scotland) and all three have VERY different accents.
In amongst those there are some very strong regional accents, particularly in England. Ice, for example, sounds nothing like I do. He's from the Midlands where they all sound like they shag their cousins (because they do). Whereas I have a home counties accent (apparently).