The best company in the UK for voice signal strength nationwide is generally Vodaphone.
The best company in the UK for data connectivity is almost always 3 (which is an Australian company, Hutchinson Telecom)
The cheapest in my experience is 3, although they're all pretty competitive.
You can buy PAYG sims at the main London airports, they're usually sold from vending machines. Or, most high streets in most towns have multiple shops and in the largest towns you'll find dedicated shops for all of the main mobile phone providers (Vodaphone, O2, 3, Orange would be the main players).
For the record, I use 3, for my phone (and daisy-chain my laptop to it) and apart from an occasionally crap voice signal out in the countryside somewhat, am very happy with them.
SIM Only data
SIM Only Voice + data
And don't forget to get your phone unlocked before you come!
G