DH has maintained his HSBC account from the age of 16 through now. I banked with credit unions when I lived in the US (which remain open accounts). Upon moving here, thanks to the advice of many people here, we went to HSBC and showed them all the necessary documents (passport, proof of residence which is in my in-laws, mail with my name on it) and for half an hour I had to fill out loads of paperwork. They issued me a bank card (chip and pin), upgraded DH's account (though I don't know to what or from what) by virtue of him now having earned income flowing into the account, and last week informed me that they couldn't confirm my tax obligation status and that I needed to fill out more papers.
As far as credit, again following the advice of members here, I used American Express' global transfer to be issued a UK AmEx, and even though it's not widely accepted everywhere, it's given me a start as far as credit history here.
Generally, I think my experience was easier than some people's, but I do find banking here more cumbersome (primarily because I could do almost everything online before as opposed to going into the branch and making an appointment with a banker).