BT have had problems. They have been switching from yahoo mail to BT mail. We lost our email for a while and our broadband. They did not even recognise that we had a broadband account as we had been "lost" at one point when they were switching accounts over. Eventually sorted and we got a good deal for infinity connection. Not sure if this is your problem, but worth finding out if you are yahoo or BT mail and logon via which one.
Good luck