If you are an existing BT customer you can arrange for your account to be moved to a new address by providing at least 2 weeks' notice and a move in date. You might need to book a visit for BT to be installed depending on whether your new home has had BT installed before or not.
BT customers will need to pay a BT moving home fee if there is no BT line in the new home, if the house does not have an aerial or if a BT Phone Package needs to be activated. The BT moving home charge covers the installation and activation costs.
If you are moving home and want to leave BT, you will need to use BT's standard cancellation process which involves calling them and potentially paying an early cancellation fee.