Hi, the same issue has happened to me, I have called BT and they couldnt locate an account nor an overdue bill. the account was terminated mutually as bt couldnt provide a stable connection and where providing me with a credit each month.
Welcome to the BT Community and thanks for your post!
I'm sorry you're having to chase this. I appreciate the amount of your time you've taken. Have you contacted Equifax directly to raise a dispute with them? That's the correct process. I have included a link below with more info.