Cheap pay-as-you-go calls, texts and web access are available from giffgaff, which uses the O2 network. To get a free sim card click here.
The deal is as follows (Feb 2012):

Use the link on this page to order your free sim, and you'll get £5 extra credit when you activate your sim.

This appeals to my luddite tendencies. Bung the giffgaff sim card in an unlocked old handset - be honest, you don't need a shiny new phone, you'd only put it in the wash or run it over anyway! You can then have cheap calls and texts, O2's network coverage, no contract, no insurance, and use up one of the UK's truly huge stock of disused handsets. In my experience giffgaff make transfering your old number simple too. An additional benefit is that if you use the giffgaff links on this page I get a little bit of free calling credit too...