Banks and credit card companies both need to be informed when you are moving house. Give your bank / building society plenty of notice of a change of address so that they can amend your details in good time.
Confirm with your bank and any other financial services organisations that you are moving home and advising them of your new address and amending all transaction information. Some will want you to visit your branch in person; others will send you a change of address form if you telephone a central number.
They will almost certainly require you to send in some form of ID such as a passport or birth certificate as well. Don’t forget to inform credit card companies, store-card companies and loan companies in the same way.
If you have any loyalty cards, let the administrators know of your change of address so you’ll still receive your bonuses. If you own any shares, inform the registrars so that share certificates and options to sell / buy all reach you within the required timeframes.