Pay As You Go (prepaid) sims are available everywhere. Plenty of choice of carriers, and can be topped up in small stores, supermarkets etc.
You may be asked to register the sim when you purchase it, although I don't think this is very common.
Pay As you Go Mobile Broadband likewise is common. Do you already have an unlocked USB modem? It can be tricky to top up some mobile broadband accounts, unless you have a UK issued credit card/debit card - or at least that's what I found a year ago.
Plenty of competition, and thus choice and cheap prices in both mobile sims and mobile broadband.
O2 , T-Mobile, Three, Orange are the main carriers, with plenty of other smaller carriers reselling their services.