I have almost exactly the same problem with BT and their customer service. Tried using their advertised methods of bill payment without success - over the phone, on their website. Eventually my wife had to take time out from her work to go to a "Paypoint" shop and pay it. We spent many hours on the phone trying to speak to someone at BT with an inkling of common sense - no chance !
We had planned to arrange a direct debit payment schedule but the BT eejit who took my call managed to cut me off and we never spoke again.
On one occasion, my wife and I stayed on the phone to BT for over two hours. Eventually being automatically cut of 20.00hrs without having spoken to anyone ! I
I spent more time held on the phone to India than I do to my mother.
When I initially inquired about getting a line installed, I was quoted, and charged, about £190.00 which I thought was very steep as the property had previously had a line and still had the BT wall box. The engineer turned up on the wrong date and my wife had to leave work to let him in to check the box. This took a good 10 minutes of his time.
Then when it came time to pay the bill, none of their methods worked despite trying them many, many times. By this time the bill was overdue and we had to pay as above.
We then got correspondence from BT (after the bill was paid) advising us that our line was being terminated and they were charging us about £130.00 for the privilege.
We heard nothing further for a while until we got a demand from BT which we responded to in dispute over the termination charge. We are agreeable to a reasonable late payment fee but not a termination charge which was due in the main because of their inept quality of service.
I then contacted them through their website complaints system to advise them of the above. the reply I received was, to put it mildly, a farce.
They offered to re-connect us if we paid the termination fee AND a re-connection fee. They would then "consider" rebating some of the charges at a later date.
Needless to say this went down like a lead balloon and we are now being chased by debt collectors.
If there was an alternative land line service to BT, we would gladly choose it. We don't have cable in our area so BT pretty much have the monopoly where we live.
I have written to the debt collection agency today and we'll have to see what the outcome is.
I'll keep your posted