This is how it worked for us. We went to HSBC and they were kind enough to allow us to open an ISA (Instant Savings Account) right away, which allowed us to have a bank account to deposit salary, and cash cards to withdraw money. No checking or credit cards yet, but the ISA account was acceptable to the estate agents when we started looking for a house. Once we had our rental agreement we went back to HSBC and they opened a full bank account (chequing, debit/Switch cards, credit cards) for us, jointly (even though I am not working.) They just needed our rental agreement, Bret's work offer letter, and our passports to open a full account. So, check different banks and see how flexible they are. We tried Barclays first and the person there wouldn't even give us the time of day!
Good luck,
Stephanie