umm as a guy from britain i'm a bit insulted you'd generalise us that way. there's no such thing as a british accent. There are dozens of accents:
Kent, Northern, Scottish, Welsh Valleys, Liverpudlian, Birmingham, Yorkshire, Lancashire, Northern Irish, Cornwall, Cardiff, Herefordshire, Leeds etc. etc.
London has a few accents itself from the "British accent" as americans know, the way posh londoners talk, to Cockney, the way common Londoners talk.
I don't think you can actually learn an accent online, you'd have to spend time with someone who had the accent.