I haven't been in a few years. I remember the British Museum being free, but then having to pay for a map of the museum, but still probably cheaper than if they charged admission. And like someone mentioned before, St. Pauls is most definitely not free! For me, who traveled extensively through Italy and France, that was a shock!
For a trip I am planning, I looked on Lonely Planet and they had sort of a breakdown of expected costs... scroll down on this page for the London one:
http://www.lonelyplanet.com/worldgui...oney-and-costs
The travel guides from Lonely Planet and Lets Go tend to focus on budget-friendly travel options. It may be worth buying one, or looking through them for restaurant ideas and other cost-saving tips.
Have an awesome trip!