Paying for calls when phone not properly disconnected

SBL

Does anyone know if phone companies automatically disconnect phone lines when calls have been silent for extended periods? i.e. if you forget to disconnect the call yourself.
We have recently had a problem with our BT bill. A local call was made at 8pm one evening for a few minutes but the phone was not put down properly and the error was not discovered til the following morning - BT charged us £35 for a 12 hour call (we got the first hour free from our unlimited anytime package!!). When I called 150 to speak to customer services the operator said she thought there was an automatic cut-off on lines which were completely silent for more than 20 minutes. This seemed to make sense - what if we'd gone off on holiday for a week?! Sadly my follow up call when I'd heard nothing for a couple of weeks was answered by an extremely rude operator who said no such cut off existed and BT were not going to pay for my mistake!
Can anyone shed any light on this? Has anyone had any simlilar experiences?
Thanks
SBL

Hazzanet

http://www.btwebworld.com/sinet/351v4p5.pdf

7.12 : When a call is ended by the called terminal, the BT Network interface will detect an offline condition and initiate a time-out process lasting between two and three minutes. After the time-out period has expired, network initiated clearing is provided to the calling terminal.