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.
This may not be much of a secret but deserves a mention. I find it hard to go anywhere near this place without having to go there. Freshly baked Beigels hot salt beef and it never closes, 24 hours a day 7 days a week.
I've had a love affair with the BT Tower for some time now. Unfortunately entrance to the public was shut in 1980, but earlier this year I was invited up to the top, where the revolving restaurant once stood. The views were absolutely breath taking.