If you are an existing EE customer you can arrange for your account to be moved to a new address by providing at least 3 weeks' notice and a move in date. You might need to book a visit for EE to be installed depending on whether your new home has had EE or BT installed before or not.
EE customers do not need to pay a EE moving home fee.
If you are moving home and want to leave EE, you will need to use EE's standard cancellation process which involves calling them and paying an early cancellation fee.