Firstly, you have to send them a letter giving the account number and state the date that you wish to close the account. You are also likely to have to provide them with some sort of identification to confirm that it is the account holder that is closing the account.
Most banks will require that you give them a period of notice before closing an account, usually a fortnight or a month. If there is still a balance in the account you will have to give them details of how they can pay out that amount, if the account is in debit you will have to come to an arrangement to clear the amount.
If it is a current account rather than a savings account you will have to make alternative arrangements to continue having standing orders and direct debits paid.
Closing a current account can require a lot of thought, it is generally best to get your direct debits and standing orders transferred onto a new account before you close the existing account. If you fail to do this, you could face charges for missed payments.
Once the account has been closed you should ensure that all paperwork related to the account is destroyed, preferably using a shredder. Identity theft is a growing problem with criminals increasingly able to make maximum use of minimum information. With a statement or bank account they can create a new account which could prove expensive or time consuming for you to resolve.