How does this scam work, please? An application was made to the original provider (BT) a digital computer line in addition to the existing copper line to my home address in a block of flats A (false) name was used to promote the application.

BT should have given me written notice of the application but this was CREATED BUT NOT processed by snail mail until after my telephone account was terminated!

In the meantime an account in the name of the digital line provider arrived at my home address 

On promptly complaining to BT , they arranged to open a new account with a new telephone number to be activated in 10 days later. After the new phone line activation, BT undertook a number change to re-install the original number 

In the intervening period the original number had been suspended.

What have I overlooked. I know I need to follow the money but since I was never going to pay for the unwanted digital line, how and who else expects to make money from this scam?