The last time I was in London, in December 2010, I visited the Churchill War Rooms (also called the Cabinet War Rooms). The most fascinating room for me was the Map Room, because of this massive map pinned across an entire wall with pins plotting all the war-related activities going on across the Atlantic. You could see hundreds of tiny holes across the map, where the pins used to sit. It was just amazing to see just how much activity there was during that time.
Read more about it on the Churchill War Rooms website.