First, get a bank account. That's really going to be fairly necessary. I got one at Lloyd's TSB without having to prove my address (although I used my temporary housing as, well, the temporary address). They're quite friendly toward immigrants. A bank account won't strictly be necessary, but it'll probably make things easier.
My wife and I found a place within about 3 days, using Gumtree and Findaproperty. There's a large amount of rental availability, although the selection appears to be a bit poor. We compromised a fair bit (we're paying a bit much for a small spot, but the location is wonderful), just to find something quickly, but it worked out. Most of the people we spoke with were independent owners and not estate agents. Of the properties we visited, no one really seemed to mind that we were recent immigrants. Most stated that they wanted between 6-8 weeks deposit (plus 1st month's rent), but that if we could make that we'd be fine. Both of us had jobs, however, so I'm sure that also made it a bit easier.
All in all, it was a far less painful process moving here than what I had feared.