Get Time Out Magazine
Time Out, the "arts and entertainment weekly" comes out every Tuesday. It is an invaluable listings journal proving details of that week's art, comedy, dance, film, music, nightlife, sport and theatre events, amongst other things, and will certainly give you ideas as to what to see and do, and help you plan your time in London. Time Out also have guide books to London, as well as a London Visitor's Guide.

Free Newspapers: The Metro & (now!) The Evening Standard
The Metro is a free morning newspaper that can be picked up in London Underground stations, usually until about 10am (when it runs out). The news is a little on the mind-numbing side, but the paper also has some listings details, film reviews and similar.

London also used to have two quite entertaining evening papers, London Lite and The London Paper. Both reasonably good on the entertainment/nightlife front, they both ceased publication in 2009.

However...London's long-established evening paper, The Evening Standard, then became free in 2009! (It was previously priced at 50p.) Be sure to pick up a copy at Underground stations from about 4pm onwards; it's also available in some (but by no means all) supermarkets.

Go Sightseeing by Bus
As long as you pick a route in Central London, sightseeing by ordinary London bus is very cheap - only 90p by Oyster card, or £2 for a cash fare! Sit on the top deck and you'll have a great view of some of London's sights, and if you see something you'd like to explore a little more of, you can just hop off.

Watch in the audience of a TV show for free
You can get free tickets to be in the audience for a variety of BBC television and radio shows. Check the BBC Tickets website for what tickets are available, and how to obtain them.

Tickets for some non-BBC shows can be obtained from Applausestore.com, TV Recordings or the Hat Trick website.

Attend a movie premiere!
Or at least, stand outside the cinema before the start of one... The Odeon in Leicester Square is where a great number of the British premieres for blockbuster movies are held. Just turn up (you may have to get there quite early) to try to spot a few celebrities. We will not be held responsible if they're of the D-list kind. Your best bet may be to wait until a Tom Cruise movie comes out - he's quite famous for spending hours (literally) meeting his fans outside these events, signing autographs, calling up people's mothers on mobile phones...