Shop around for the bank account that suits you best. The type of account you need will depend on what you want to use it for, savings, day to day expenditure or something else.
You'll probably need to provide various identification documents such as a passport or driving licence when you open a new bank account. For information on bank accounts see Bank accounts (on MMC).
When you apply for a bank account the bank or building society will tell you if it plans to run a credit check on you with a credit reference agency about your suitability to have a bank account. If your former spouse or partner dealt with most of the household finances, you may not have built up your own credit history. In this case, banks may be reluctant to let you open a current account (which typically comes with a debit card, cheque book and the possibility of an overdraft).
You may be able to open a basic bank account (which has a more limited range of features that let you manage day-to-day transactions without going overdrawn). For more information about basic bank accounts, get see Bank accounts.