We are in the UK several times every year to see family. We have an older unlocked AT&T iPhone 3GS and when in Britain we use a contract-free SIM card from Virgin Mobile. We've just bought a new iPhone 5 from T-mobile that lets us do the same. Verizon and AT&T phones are locked until your contract is up, and the advantage of a contract-free, unlocked phone is why we went with T-mobile.
In the UK, you can get SIM cards just about anywhere. You could go with a prepaid card, or a contract-free month-to-month plan. We use the latter, it's much cheaper and more convenient.
(by the way, I usually get a pre-paid card for my iPad as well, both in Britain and in Germany. I have a little wallet in which I keep all the spare SIM cards, and I swap them in and out as I travel)