It depends on if the flat is available immediately. When were were looking, about half were. The other half had people living in them, so if we chose them we'd have to wait for the current tenants to move out. This flat was like that. We looked at it in late September, handed over the deposit a few days later, and moved in in November.
You will need references from previous landlords, which sometimes can come from overseas LLs. We were able to use previous one. They will need to do a credit check. I am not sure how that works with the newly immigrated without a British resident partner. This can take a week or so. If you can't find a landlord, either private or through an agency (really recommend you be careful with agencies) that will take either of these sets of credentials as good enough, a larger deposit based on several months' rent will sometimes do, but if you've already found a job, and you have good US references, you might not have to worry about it. Setting up a bank account would help, and you will at least need one that they can draw payments from. Most things here are done through automatic drafts, and most LLs or agencies would require that you pay that way.
The other thing that might hold things up is contents insurance. If your flat has furnishings of any sort, even just something like a washing machine, the LL/agency might require contents insurance.
Oh, and some agencies offer a "complimentary service" where they turn your utilities on. Don't bother with this. All they are trying to do is get you to switch the provider to the companies they get a bonus from.
I'd say realistically look at at least a month before move in. You might be waiting a bit more or find something that will take less, but I think a month is pretty much a realistic time frame.
