What should I do with a 13.5 hour layover at the London Heathrow Airport?

I would like to see London and I was thinking of taking the underground train. Unfortunately my layover is from 10:05pm - 11:30am (with the train it seems like I would have time from about 11:00pm - 9:30am in London) so not the best time to do things. Is there anything I would be able to do? Would I be safe walking around London by myself late at night/early morning?