Not sure if they still do, but O2 used to offer a sim-only deal for people with bad credit. Then if you paid it on time every month, after a while they would offer you a normal contract as they have seen that you will pay it.
After my teenage son running up a huge bill on contract, I brought a phone and got a giffgaff sim card, its only £10 a month and that's 500 minutes, ulimited text and 1mb of data. only downside is you have to buy your own phone. I got an iphone 4s from ebay for £200 for him and works out cheaper over the typical 24 month contract that getting a 'free' phone with a contract.