Open Garden Squares Weekend happens annually in June, when many of the city's locked, off-limits garden squares open their gates to the clamoring hordes. Public as well as private gardens participate, and a number of them host fetes, food and music. It was hands-down the best £10 I've spent in London, not only because it allowed me to go places I'd never normally be able to see, but also provided a beautiful new way of discovering the city. Your £10 buys you an entrance ticket and a thorough guidebook with hundreds of gardens, handily sorted with maps, so you can plan your weekend. There are way too many to see all of them, so I narrowed my search by 'secret gardens' (ones normally closed to the public) and vicinity to other places. The best part for me was being able to enjoy the time and spaces, so I wouldn't recommend trying to cram them all in unless you're a really keen gardener. It actually is possible to get garden fatigue. (Ho hum, another gorgeous rose.)
It was neat to be a tourist in a way that also felt very local/national - Open Garden Squares isn't on most international tourists' radar (or even most Londoners'). If you're around, I highly recommend it for a novel way to see the city, and to enjoy the bits of nature that are beautifully preserved and cultivated between the cracks in the urban pavement.