You can apply to switch your account using the current account switch guarantee that almost all banks will be part of ->
https://www.currentaccountswitch.co.uk/Pages/Home.aspx
You give your new account provider your old bank details, they switch everything over on a date of your choosing and your old account is automatically closed and everything carries on from the new account.
If you don't want to close the old account or don't want to use the switching service its a case of you contacting everyone that pays in or takes a DD out of your account and asking them to swap to the new account details.