I do think there are some checks made even on a basic account.
A friend of mine recently opened an account with the Co-Op - she hasnt had a bank account for about 10 years and still had to jump through numerous hoops to get one. The problem was her address, although she has lived there 15 years, the house doesnt show as a house let in parts and this took some sorting. Her proof of benefit had to be on original stationery and not the photocopy she had requested from the benefits office. I dont think they will refuse one but they will ensure your ID is spot on!!!