I switched form pay-as-you-go to a monthly contract (O2) this January. At that point I'd been studying in the UK for 2 and a half years. But the only thing they were interested in at the shop was to check my credit history by using my bank account details (my UK account, that is, which I've had for the whole period of my study). I didn't have to provide them with proof of my address or anything. I'm from the EU though, but I doubt that'd make much difference since they weren't interested in where I came from. Also, a friend of mine got a contact already during his second year of study, and he's not a UK student either.
If they won't let you have a contract right away because you won't have credit history as you'll only have had your British bank account for days, then maybe just get pay-as-you-go and switch to contract in a year or so.
Edit: just realised it could be different if you're planning on getting a phone with the sim card as well. I just bought the sim card for a phone I already had and so am not paying for a phone while paying for using it as well. Don't know if it makes any difference.