I'd imagine the new bank would need proof of id (passport etc) possible pitfalls could be a credit check but there are many more informative and knowledgable peeps around.
for any account other than the basic account you need to be on the electoral roll i think. you'll need to take id & a couple of utility bills possibly.
also you would need to chjeck how much notice you would need to give to amend a doirect debit or standing order instruction and also how much notice you would have to give your employer to tranbsfer your wage into the new account