Perhaps in answer to some of the comments?.
BT like most service providers have various terms and conditions (small print) that most customers never read (I usually don't).
BT will not provide (like most service providers) an information service, unless it is usually in their favour or perhaps a regulation/service alert. Years ago, when the GPO/BT had the monopoly they had the 'Low' user tariff/rate, which some people were able to obtain a refund on calls, if it was below the line/service rate. Many various rates and supposed short term incentives nowadays, have or are proving very confusing for the public to understand. I suppose that you can put this down to 'Good Marketing'?.
With regards to the BT Customer Care person's persistent manner, he might have been trying to 'screen read' BT's terms and conditions, by suggesting a transfer. The ISP I use will do this for free, otherwise a fee will be charged. What I would suggest, is look at the contract start and finish date, and see if this contract is in force. Quite a number of cases, the contract comes to an end, and the service provider continues with the service on a 'rolling' basis. In which case the customer is at liberty to cancel at anytime without penalty.