We spent a week in Britain in May and were treated with courtesy and respect everywhere we went (London, Bath, Stratford-Upon-Avon, Oxford), notwithstanding our Texas accents. Relax and have a great time. Remember that you can run into a jerk anywhere!
You could spend a week in London and not see it all, but if this is your first trip, don't miss the Tower of London.
Great advice. My parents were in Britain over 9/11/02 and said the british people were so friendly and expressed a lot of condolences about 9/11/01.