Eccentric and surprising house and museum of architect Sir John Soane. Mostly unchanged since his death over 180 years ago, it is full of atmosphere. Also have spotlit, late night openings.
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.
One of the main sources of inspiration for my work are unusual objects, vintage toys and tools. A great place to find them is this genuine car boot sale, which is clear of 'bargain' toilet paper and questionable cosmetics. Another plus are the comparatively sociable opening hours. (it starts at noon… )