I'm not in a position to endorse Jamjaw but I can endorse giffgaff. I have two giffgaff sims (1 phone, 1 iPad) that I use when I'm in the UK - they work fine and the rates are good. It works on the O2 network but is run (administered) by volunteers (such as Jamjaw) who send out sims, provide user support etc. If you order a sim, need to make it clear whether you need a sim, a micro sim, a nano sim etc.

You can also buy top-up vouchers at any O2 store (just ask for a giffgaff voucher). Once you have the phone number, you can register online, top-up online (thought that requires a UK credit card), buy 'goodybags' (pre-packaged minutes/text/internet) etc. All in all, has worked well for me.