BT will own the line to the exchange and the broadband interface - they will rent the Broadband to your service provider (Tiscali probably) and will not cut the Broadband service until Tiscali tell them to do it. From experience it takes Tiscali several weeks to ask BT to suspend internet services.
If you move into a property where Tiscali Internet was being used and want to use BT Broadband you have to wait for Tiscali to talk to BT - then wait a little longer for BT to disconnect Tiscali - then wait some more for BT to connect any new service. Could be up to six weeks for all this to happen!
Peccavi, October 2008