Hi
Just a little more to add as there's a little more to this.
You can purchase Quad Band mobile handsets. These will work in the USA and UK. If you get one which is already 'unlocked' then that's a bonus and it means you can pop in a USA SIM when you are USA side and a UK SIM when in the UK.
I have a Samsung T249 Quad Band handset which I bought in Las Vegas when I lost one of my UK handsets for aroudn $129 USD. It was from a TMobile shop and 'locked' to that network.Upon returning here to the UK, I had it unlocked and was using it on the Tesco/O2 networks. It's sitting here doing nothing, so if anyone wants it, £30 delivered?! (just bumped my advert in the For Sale section!)
Warren - as per above and other responses, you'll need a Quad Band handset. However there is a caveat and that is to check the frequency bands of the handset you buy and the frequencies of the UK cellular networks. Here's a site which shows those;
http://www.ofcom.org.uk/static/archive/ra/topics/pmc/document/licencetypes/cellularinfo.htmRight now, the UK is 'just' about to have it's first 4G network go live and that requires one of the very latest handsets which is 4G capable - theres only 4/5 handsets to choose from here and I believe, they're UK specific for the frequency band 4G services will be on - don't be tempted to pick up a USA 4G handset thinking it will work here.
Brigette - As per above and other responses as well, if you purchase an 'unlocked' iPhone from the US, you can indeed use it over here. You'll need one of those 'iphone' specific small SIM cards when you get here to the UK and as mentioned, you'd probably pay much more for a PAYG small SIM at the airport, so a trip to one of the local mobile phone company shops or carphone warehouse etc would be needed.
Cadenza - to an extent and perhaps up till around 2002'ish, I'd agree with you, but since then, the US 'mobile phone' market overtook and surpassed the UK and in the years 2002-2008/9 was comfortably ahead - for technology, price plans, flexibility and choice. I had the pleasure of being one of the UK's beta testers for the 3G network around Q1/Q2 2002 and it did take a number of years before 3G was as good as it currently is. I was also playing with 4G in the US in 2009 - Las Vegas specifically, although just a few areas of the this city and a few others were 4G capable, the network has grown there for 4G quite well. Here in the UK, more dithering around and politics and red tape have meant until recently, late 2013/early 2014 was the likely 4G availability date. With some 'last minute' scrabbling around, the first Everything Everywhere 4G network goes live in a few days time. The rest of the companies have 'sort of' put their differences aside and agreed on rolling out some 4G network during Q1/Q2 of 2013 I believe.
Lastly, at long last, there is a very nicely priced, fully featured Acer smartphone that has Dual SIM capability. It's Android 4 powered and has some nice specifications for around £164 !
http://www.expansys.com/acer-liquid-gallant-duo-black-234432/I'm going to be placing my order very soon!
Cheers, DtM! West London & Slough UK!