When I was setting up the laptop to work in the Norfolk hideyhole, which is with a different ISP, I forgot that it was still plugged into the BT line here.
When I'd finished entering the settings, it set off and connected quite happily to PlusNet. The "contract" here is with Pipex.
I was a little surprised - I'd assumed that only a Pipex connect would work on the "home" line. But then I found that there's also a BT "ADSL test" that can be used if your ISP seems to be "off the air" and you want to know if it's you or them.
So maybe you can connect to a different ISP, and all this migration stuff is bureaucracy - or "billing".