Well, it, of course, depends on your interests. I was there on a theater program, so I spent a lot of time in various theaters.

If you like art, I highly suggest the Tate Gallery. It's my favorite.

And set aside at least a day for the British Museum.

I also loved the Museum of the Moving Image.

And St. Pauls Cathedral!

And finally, if you get a chance, eat at Wagamama. Yummy!