The process for getting a bank account changes CONSTANTLY! Do some research into each of the main banks' policies just before you move over. The main banks who don't need proof of address at time of writing are:
In order to open an account with most banks you will need to book an appointment. Check out their websites for all the details and to book an appointment.
The bank you'll probably hear everyone talking about is Monzo. Monzo is awesome because it's simple to open up an account, but what's even better is that you can use your card all through Europe without being charged currency conversion fees. It's an internet based bank, so it might be worth opening a standard bank account too, but definitely one to check out.