For me, getting a bank account was the single most difficult thing about moving to the UK. It took me 6 months to finally find a bank willing to offer me an account, because I didn't fit neatly into one of their predefined categories.
The crux of getting a bank account for me wasn't that I didn't have a solid banking/credit history in the US, but that it was difficult to "prove" my address since we are living in student housing as my husband is a student. I didn't have a council tax bill, electric/phone/internet bill or anything else that they would take as proof of address. They wouldn't even take my pay stub! Not a letter from my landlord, not a letter from my employer. I'm not sure if banks are so rigid by choice or by requirement of law, but either way it was not a fun process.
To get a bank account you will need: proof of identity (passport) and proof of address (council tax bill or electric/phone/internet/water bill showing your name and your address). Depending on the bank, they may also want to see three months of bank statements from your US bank and/or a copy of your US credit report. If you have all these things, then you can pretty much walk up to any high street bank (NatWest, Barclays, HSBC, RBOS, etc) and get an account the same day.
What I ended up having to do was apply for an offshore account through Lloyd's TSB. It's called a World Wide Service account and is especially for foreign nationals who have resided in the UK for less than 3 years. Works just like a regular Lloyd's TSB account, but is classified differently under UK law (don't ask me why) and thus is subject to different rules about what can be accepted as proof of address/identity/income, etc. I *highly* reccomend it. At the end of three years, if you can prove you have a visa to extend your stay, then they automatically roll you over to a regular UK current acount. Very nice indeed!
Whatever you do, come prepared and bring more information than you think you'll ever need. Good luck!!