London is great... the only problem is that it's really expensive. Just out of curiosity, what site did you go through to get your tickets? $400 is dirt cheap; most ticket from non-major airports (i.e. anything but New York) cost around $700. I don't know what airport you're flying in to in London, but since more or less they're all the same, here's my tips:
Head out of the airport and find a taxi. Tell the driver that you want to find a 'youth hostel'. Expect to pay around 20 quid... around 35 US dollars to get there. Once you're there, you've got dormitory style bedding for around $25 per night.
The next morning, get a pass for the buses. It'll run you around 20 bucks for 3 days (unlimited), but since you plan on staying in London then it shouldn't matter. If you were going to Amsterdam or elsewhere then things would be a LOT cheaper, but as the UK is more expensive then I guess you have to deal the hand you're dealt.