I had to move a few months back, still having 8 months or so left on a cable contract.
After some confusion, in a nutshel someone at VM demanding 240 quid off me to end my contract. Second sales member, was excellent...looked at my new details and said, yes you may not have cable but we can supply adsl, all I need is a BT line. No end of contract fee, as i was staying with VM.
Find out in your new build, if the sockets are already installed and there is a dial tone. If there is, connection to BT should be free, It was in my case, moving into a new build.
If they need an engineer out to fit the line it will be 125 quid
Once I had the new BT contract and number, gave vm sales a ring and everything was set up in a week. They even allowed the new router to be delivered to my works addy.