If you want to change your business or trading address, you just need to make sure that you tell all of your business contacts. This includes:
Suppliers and manufacturers
Service providers - utility companies, insurance, couriers, etc
Banks, lenders and investors
Tax departments within HMRC
Local council - if you have any licences or permits
You should also make sure that you update your website and social media accounts with your new business address. It would be a good idea to send out an email and post an announcement on your website and social media ahead of the move, just to make everyone aware of your impending move.
If your business is set up as a limited company and you wish to move your registered office to the new premises, you must tell Companies House as soon as possible. You will also have to update your registered office details on your website and company stationery.