Imho BT bring these things upon themselves, or at least, upon their customers.
When you find yourself talking to what is obviously an amateurish Indian call centre, you can't assume it's fake, as BT do actually outsource to amateurish Indian call centres.
When you get an unsolicited robotic phone call, claiming to be from BT and wanting to discuss your account and payments, you can't assume it is junk. For BT really do make unsolicited robotic calls to their customers, to try and jolly along bill payments.
I am not surprised that scammers find it rewarding to put some effort into cashing in on these weaknesses.