We just returned two weeks ago from London and had a fine time. It most certainly is an interesting place. Weather was not the greatest as one can expect this time of year but we dressed accordingly and managed to see all the major sites in the short time we had there. (One full day of touring London). We took the city tour bus that you hop on and hop off at any location for a 24 hr period. The tour was 2 1/2 hours long and passed the major (must see) attractions. Then we went back to the one's we wanted to spend more time in and got off the bus there. It was a practical and cost effective way to see London in a short time.
If your staying longer there is much more to do, not to mention some great theatre.
Have a great time in London. The one thing I am glad we didn't do is rent a car. Driving in London is actually worse than driving in NYC when you don't know the town.