canopy_gone,
Whilst I was there I lived in East London. I pretty much stuck to a budget of approximately £40 per week for food, however I often did not spend that amount, and my rent was about £380 per month. Therefore for the duration of my stay in London to live cost me around £3780. I had a bicycle for transportation, so no real transport costs, apart from the odd trip home to visit friends and family.
Good Luck.