Getting lost is an age old suggestion but a good one. Put away your cell phone or your A-Z and just wander around. I still do this regularly even though Ive lived here for nearly 10 years. London is a big city and it drip feeds you its secrets sometimes. You will come across things you wouldn't usually, in amongst the Starbucks and pret a mange there are some amazing sights. Just 'being' somewhere is a great experience and one no guide book can help you find.
I grew up in the countryside, and if you're ever in need some instant escape from the city, this place is like a time warp. It's a huge space full of over grown mausoleums and graves, feels like a movie set. They also do tours.