FWIW, if you go through an agent they will run a credit check anyways. No getting round it. Good character references from reputable non relatives can help there, as can that for private. If you rent privately, depending on the landlord, some will want credit checks, some will want 6 months rent in advance, some won't. It really will depend on the luck of the draw on that front.
If you have a UK bank account, can pay 6 months rent up front (and make sure any deposit gets paid into the deposit scheme or else its dodgy) and can satisfy them you can cover the bills etc then you should find something. Just be prepared that there could be a lot of people after the same sort of thing, renting without credit history etc and so it could take some effort and a bit of time to find something.