There is a lot to see and do in London, as mentioned above. However if you're considering going around London as well I would prefer a day trip to Stratford upon Avon or Oxford (or perhaps Cambridge).

I know that there are also day trips to Stonehenge and Salisbury. It is a bit long, but might be interesting for you.

Another suggestion I could make, is look out for haunted walk evening tours. I'm sure there are quite a few in London, and they will give you a somewhat different perspective on the history of London.