Firstly contact Tiscali, and inform them that you wish to terminate your contract on a specific date(eg the end of your contract.)
Secondly request a MAC code within 30 days of your contract ceasing.
Contact BT and ask them to reinstate your line on the day of the end of your contract with Tiscali, or as near as possible.
Contact your new ISP and give them the supplied MAC code and tell them to start the new BB on the day of termination of Tiscali contract, or as near as possible.
Bear in mind that all these things will take time, so give as much notice as possible, in writing where applicable, to make the transition as smooth as possible.
Be prepared for Tiscali to make some offers to keep you as a customer.