The first thing you have to think when you will prepare your trip, is the place you are going to sleep.
I am sure you won't be happy when you will know prices for flat in London. In average, I think it is difficult to find a bed (in a flat) under 80 / 90 £ a week.
In order to help you to find the best solution, you will find in theses subpages my experience in London accommodation and other stories and tips from several friends...