Hello Manc08,
Sadly some providers still use the term "you can move the connection" however depending on how involved your subscription is this can very simple or a hassle. Having to phone the sales line and set up a new connection is unacceptable as a provider if they say you can move home without issue they should make some effort towards this.
Usually the supplier requests a reconnection fee or restarts the contract to accommodate for this. If you can I would advise moving supplier if possible or simply complain to get some sort of support from your supplier and as soon as you are put of contract, move, you are being overcharged and under serviced with that supplier.
Kind Regards,
Michael.