I'd get a phone, plus a rolling contract if you can afford it. Contracts included the price of the phone in the plan anyway, you can only save a little bit of money by getting the phone 'free' and paying x amount per month.
How many mins and texts do you need? £22.50 can be quite costly for a student, unless you are getting a good phone with it which you want. It all depends on how much you want the phone. What length of contrat too?
One suggestion could be as I said about, get a phone for like £100, then get a contract which is about £15 per month which can be cancelled at any time, then you are not locked in and have a phone. You'll find that £15 contracts which are sim only are pretty generous, but may not include internet with some providers.
I got a phone (Nokia E63) on an 18 month contract on '3' (Three), £15 per month for 75 mins, unlimited txts, unlimited 3to3 calls and unlimited internet. And that deal was back in August.