First of all Britain has a million and one different accents just like America does. Just like someone in Queens New York doesn't sound like someone from Alabama, Someone from London doesn't sound like some from Liverpool.
Only a hand full of British people speak in High Class Cambridge accents. The average person you meet in Britain doesn't sound like that. Its only in your Holllywood movies that everyone talks like that.
The English language and accents are always changing. How people speak and use words from 100 years ago is different to how people speak now.
In london the tradional cockney accent is dieing out. Most young people speak in jamacianized english as influenced by immigation over the last 50 years.
Lots of British bands in the past most likely sing in American accents as the music they growed up was by american singers and bands. The Beatles and Rolling Stones listened to Chuck Berry and Little Richard so tried to sound like them.
Some American bands like The Killers Sing in British accents.
Not all bands and singers do sing in american accents. Its more noticeable to you guys because the bands that make it big in the states may sing that way.
I can give some likes to British bands music viedos that do sing in their own regional accent.
http://www.youtube.com/watch?v=30w8DyEJ__0 - Artic Monkeys- (Sheffield Yorksire)