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 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.
Though the city is amazing with a lot to offer, of course it’s great to have your own hideaway. My room is essentially my studio/desk space too and the hub of my creative activities.