if at all possible not to expensive. Answers on a post card.
No one knows -- which is why no one knows about them.
The Hunterian Gallery, as long as you aren't squeamish.
Beanotown is on the Southbank for a couple of months.
The old operating theatre and herb loft is my favourite unheard of place to take people as they visit http://www.thegarret.org.uk/
For free things i would say any of the city farms are a good way to kill an day or you could go down the Parkland walk for some vegetation and an former railway line in the center of the city. If you go from the alexandra palace end to finsbury park you can have a pint at the faltering Fulback when you stop as well
i've heard that going on r/london and asking what are the best things to do in london NEVER HAPPENS...so perhaps do that...
The best thing to do in London is to sit in the park at a summer weekend with some cronies with a few drinks. though everybody knows that this is awesome. Luckily we have ample park space for everyone.
session in my front room, playing Dark Souls for 13 hours at once while eating a whole package of Screwballs out of the freezer.