Miss S, my travel companion and general bad influence, and I in front of a bridge in London. Not the London Bridge.
So, one thing to do there? Get to Gatwick and take the first RyanAir flight outta there.
Seven (gah!) years ago, in my own travel hey-day, RyanAir offered one-way tickets for $1euro. Amazing. These days, the lowest fare is closer to $10euro one way, but still not a bad deal. It gives you a great starting point for a cheap European trip because you can often find cheap flights to London. Sure, you are herded like cattle in the plane, but c'mon - it's cheap!
If you insist on staying in London, I have two suggestions: get a candy bar. The British know how to make sweets, so you can't go wrong with your choice. Also, see a play or something, you lame, uncultured American.