Go to the Tower of London somewhat early so you can get a tour with the Beefeaters. They are dressed like the liquor and most are really funny and give great tours.
Also, British museum is a good collection of what the British have stolen over the years.
The Imperial War Museum is good, but the Cabinet War Bunkers were Churchill and gang commanded the war is really cool (near Westminster Church).
And hit as many pubs as you can. The British, unlike Americans, drink on their way home from work and have last call at 10:45. You'll have to hit a club or restuarant for drinking after that. But, it makes things easier in the morning if you quit around 11:00 and head home to relax for a bit.