What are the best spontaneous / no-book things to do in London?

Basically, I have health issues that flare up every now and then, which makes it hard to plan stuff as a lot of the time I'll end up cancelling, losing deposits etc. But when I feel fine, I want to make the most of things.

I've lived here for about 6 months now and am aware of all the normal touristy stuff / landmarks / parks etc but was wondering if I have missed anything. It could be a game, attraction, event, anything. And as with anything, the cheaper the better!