I was actually at my 3rd bank trying to open an account, but without any other documentation than my passport & visa. I think it was Halifax. The guy I was speaking went in back for a bit, and per usual said "I'm sorry but without proof of address we can't open an account for you." When I started lamenting my sense of defeat to him about UK banks, he said "okay look, I'm not supposed to say this, but off the record, if you go down the street to Lloyds, they have a special process for US citizens where you can just open an account with a passport." Sure enough I went down the road, and after making yet another appointment (an appointment to open a bank account? really Britain…), they confirmed that indeed they do open accounts for US citizens with just a passport.
So I feel pretty confident in recommending Lloyds in this case.