I found a great bargain in the Holborn Library 20p book sale this week, “London Free and Dirt Cheap” by Joe Fullman (Frommer’s.)
The copy I obtained was an edition from 2007 but I am sure you’ll be able to find an up-to-date version quite cheap (prices from £3 inc p+p on amazon!)
There’s some classic cheap London moments here and loads of stuff we didn’t know about, e.g. Best Free Hidden Gem: The Petrie Museum of Egyptian Archaeology, lots of cheap eats ideas including somewhere with the great name of Porky’s Pantry (now sadly closed,) free oddities to visit like The London Stone, free music and concert ideas and free tickets to TV shows too.
Go out and get a copy and get ideas for having fun for (next to) nothing! P