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.
London is so vast I end up spending hours travelling on trains. They are by far the best way to travel around on and are always full of weird and wonderful characters.
I didn’t know it existed until I moved to Brixton. Brockwell Park has been a revelation to me, it’s beautiful with many secrets. Check out the outdoor theatre in the summer up by the old house - Midsummer Night’s Dream last year on a midsummer’s night was astoundingly good.
The V and A houses a public collection of prints and drawings of every kind imagineable from old master drawings to photographs, playing cards, fashion plates and wallpapers. You have to select what you want to see from the collection http://collections.vam.ac.uk/and book in advance. The behind-the-scenes route up to the study room of v and a is a treat alone (pictured)
One of my favourite places to snoop around is the food market open on a Thursday, Friday and Saturday. It's always bustling with crowds so great for people watching. You can get the best of anything here which is why it's hard to resist spending a small fortune.