The only reason I know of, which I've seen with several migrations, is that the BT changes take place before the account is fully activated on the ISP's systems, and this has caused awful throughputs until a router reboot after the account is properly set up at the ISP end.
So maybe they have a similar constraint, or even cannot complete the setup if the line is in use when they try?
You may not know that a new broadband activation requires BT Openreach to connect the line from the user to the ISP/wholesaler DSLAM and the PSTN phone service at the exchange to the DSLAM as well, to get onto the subscriber line.
As I understand it, if the phone is being LLU'ed as well then the PSTN does not get connected to the DSLAM. It is up to the SP to separate the two at their end. I could be wrong there.
In this instance I assume the phone rental is staying with BT. If not, the OP is going to get a nasty shock unless he picks it up and gets that part cancelled.