All US iphones are locked to AT&T with no way to officially unlock them as AT&T will not unlock an iphone for anyone for any reason. To use your phone in the UK would require international provisioning activated for your account. From there you'd pick a plan and carrier to use while in the UK. For any length of time, this would be very expensive. You didn't define "extended period". If a year or more, sell your US iphone, purchase an unlocked iphone in the the Uk, then you can use that phone in the US when you come back.
For the reasons wjosten explains your best bet will probably be to purchase an iPhone 4 from Apple UK (which are unlocked) when you arrive. £499 (inc VAT) 16GB, £599 (inc VAT) 32GB. (VAT increases by 2.5% on 31 Dec 10).
You can then get a cost-effective "SIM-only" plan in the UK which I think all 7 big name operators in the UK offer on a 30-day contract basis. You'll save a little money (typically £5 per month) if you can commit to a 12month contract.
If you move around in Europe the handset will be unlocked and so you can pop in a local SIM anywhere in the world.
For light use the MVNO Tesco offers 1GB data, 250mins voice (outgoing) and unlimited SMS for £15pm SIM only and the contract is only 30 days.