Go to the theatre. All of them have cheap tickets for people under 26 (like at the Royal Court, it's a fiver). Check out the work there, or at the Soho Theatre, who have good new young writers, or try the National - lots of seats are available for £10. In the summer you can see Shakespeare at the Globe for a fiver if you don't mind standing (and you'll get the best view). See timeout.com/london/theatre.

google oyster card offers. It'll be on the tfl (transport for london) website, and it'll tell you load of things you can do for reduced prices using your oyster card. Awesome. London attractions like the aquarium are 2 for 1, cheap theatre tickets etc