I had a US Motorola Razr when I came to the UK. I put in a UK sim card and used it here for two years with no problem. I just thought all phones would work wherever, However, I bought a phone here for my grand daughter in the US, had it unlocked and sent it to her. She put a US sim card in it and couldn't get it to work. When I called the mobile company about it, they told me that it was because a lot of the phones sold here are 2G while in the states they operate off the 3G. So basically a 2G phone won't work in a 3G system, but a 3G phone will work on a 2G system. At least that what I understood the person to tell me.
If you're just wanting a phone and not a smartphone, you can pick one up here pretty cheap. I bought two of them for when my family visit and paid about £20 each. I simply pop in a prepaid sim card when they arrive and they have a mobile to use during their visits.
Smartphones will run you quite a bit more. When I google payg smartphones, I see several ranging from about £75 - £200