As others has suggested, The British Museum is a must. So many amazing artefacts that we have stol… acquired from around the world. Plus it’s free to get in, although a donation is asked for.
The Tower of London and Windsor Castle are also popular tourist spots, although they will cost you, and Windsor Castle isn’t in the city, so you’d be best putting aside most of a day for a visit there.
I have visited most of the museums and castles in the last 5-10 years and even posted of my exploits here, if you’re interested in hearing it firsthand from a fellow history geek. And yes, that website is a historic relic in itself, heh.
Hope you enjoy your trip, and if you have any questions ask away, I’ve not lived in the capital for a few years but I might be able to help out.