Hi Peter,
Alas, I live on this side of the pond, but studied in London and travel there several times a year on business. I have a number of recommendations. There are the big ones, such as the British Museum, which has an amazing collection of archeological artifacts from around the world, including the Elgin Marbles (taken from the Parthenon) and the Rosetta Stone. The Imperial War Museum and the Churchill War Rooms are also great. The Crown Jewels -- together with a remarkable collection of medieval armor and weaponry -- are at the Tower of London. In terms of transportation-related goodies, I highly highly highly recommend the London Transport Museum in Covent Gardens. It includes dozens of classic London busses, rail cars, taxis from the dawn of the age of transport to the present. Also in Covent Gardens is the London Film Museum, which for several years has hosted an exhibit called Bond in Motion, which includes numerous vehicles from the Bond films. Lots of fun.
Enjoy!