As someone who has been caught by this...
After a number of years with BT I attempted to switch providers from BT last year due to a number of problems in our area with broadband speed and reliability after the 21CN upgrades. Unfortunately I was on BT friends and family and there would be a charge for terminating early. As it was only two months away, I stupidly waited to avoid the charge.
I then gave BT one months notice and everything went smoothly for the broadband, but the phone line was delay by ten days which meant BT automatically renewed the friends and family deal for 12 months inspite of having the BT line for only two days during this 12 month contract.
It took about four weeks of calls to an Indian call centre before I was able to get someone who could understand the issue rather than just say "yes I understand what the problem is" and offer a £10 refund (the early contract termination was for about £90).
Yes I got my refund but it required a lot of time talking to idiots and BT provided no compensation for the braincells that gave up during the process.
When the revolution comes, my vote is for BT staff to be first against the wall...