I guess you are ending one contract and starting another so I can see why they would claim they are entitled to the pre-stated costs of doing so. New customers at the old address, you at a different one. I have sympathy as my experiences with BT have not been good, but I can see how you got to that situation. If broadband is a set cost maybe it'd be better to have had the rent include broadband.
Best of luck appealing to their better nature, I don't think those who run the company have one. What I can say is to beware of lies and deception. Last time, I was offered a reduction in the next bill as some kind of gesture (for recompense for what they know they'd got wrong) by their customer service agent (eventually) and when the next bill arrived they had applied it only to a part of the bill, the vanishingly small voice call part !