Hi,
I've posted this resource up lately so that you can check and confirm if your actual mobile phones will work on a carrier network you may wish to buy a SIM card for
http://talk.uk-yankee.com/index.php?topic=89461.0Unlocking is one aspect, compatibility and the technical spec of the actual phone is another.
If you find that your handsets aren't compatible, you can purchase phones outright easily here and use a monthly SIM service that doesn't require you to have credit checks and get contracts. I've not purchased a contract phone for well over a decade now - just stay on a SIM only plan as the phones I use aren't available on the general UK high street - I have two Dual SIM handsets, and another difference between them is different frequency bands for the countries I'm sometimes in. When in the UK, I use different UK carrier's for each SIM slot.
Here's a couple of reputable online retailers of mobile phones where you can get different spec phones of the 'popular' ones you see advertised on mainstream media
http://www.handtec.co.uk/https://www.clove.co.uk/Actual signal coverage varies and can be quite close to you. A friend may get full strength reception on O2 and you'll stand there with one bar on EE. Move a few hundred yards and that could swap! it's less likely nowadays, but still happens.
Take a look at giffgaff as well as Virgin mobile who are 'virtual operators' - they'll use the 'actual' signal/network from one of the big players, but have their own deals etc. Same with the Virtual Network offered at Carphone Warehouse too.
Cheers, DtM! West London & Slough UK!