Fodor’s Travel Wire recently put out a comprehensive list of sites and activities in London that are free, or close to it. I’ve never spent as much money in as short amount of time as I have when I’ve been in London. The last time I was there the dollar was significantly stronger than it is now, yet I managed to blow through my (admittedly meager) savings in a weekend.
Fodor’s list includes free or cheap art museums, free concerts, and cheap theater, opera, and movies. The “offbeat experiences” are the best: look up ancestors in a public record office, visit Hyde Park or Covent Garden, or watch fishmongers in Borough Market.
Don’t forget to account for the cost of transportation when planning your budget — the Tube is not cheap, although it’s the least expensive way to get around London besides walking.