For any WWII history buffs like me, Churchill's war rooms are a must, along with the suggestions above. These are underground facilities from which England ran their operations in WWII. They are surprisingly small and surprisingly detailed. From them, I could see maps of where the German subs were that my father was hunting off the coast of Florida. And the War Rooms are not a large facility. To think a major WWII power ran their part of the war from their boggles the mind.
Should you go to Harrods (and you surely will) go to the furniture department, where they have a section called "American style Furniture." I looked at it and started laughing, and a salesman came up and asked why. I told him (truthfully) that we have the same style of furniture in America, but have a different name for it. He asked what the name was. I told him "English Country!"
In Rome, we got a good limo driver and feel we saw the whole thing in nine hours. That won't happen in London. We'd like to spend two weeks there, even though we've been there before. There is more to see in that city than in any other in the world.
Hope this helps,
Richard :) :) :)