£1000 early disconnection charge - despite notifying VM of switch during cooling off period!

Hi. Hoping someone can help or steer me in the right direction - as ive been going around in circles and being passed to multiple people on message service and calls. We decided to leave VM - We were advised by a call handler that  becuase we were technically still in contract, to change to a new cheaper contract, then to switch during the cooling off period for this new contract. We thought that was strangely good advice (surprising that VM would advise this) but it made sense. So we changed to a much cheaper contract, and then, through the one touch switch process, notified VM that we wanted to cancel our contract.

Virgin sent us an email on 18 October (within our cooling off period), confirming the date of our switch (07 November) and clearly confirming (in bold text) that there would not be a disconnection fee (specifically the email stated there would be a 0.00 disconnection fee. They have have subsequently charged us a disconnection fee of GBP 1023.66!. 

I can only think their rationale is that despite giving notice to cancel within the cooling off period, the actual switch took place outside the 14 days - however we absolutely notified them that we wanted to cancel during the cooling off period - as the email clearly confirmed. If they had told us about the disconnection charge (rather than telling us there wouldnt have been one!) we would of course have been in touch with them and it may have prompted us to change our mind. But they didnt.

Trying to explain this to the call centre team is impossible - they dont understand what I'm saying, tell me the email was automated and incorrect (!), then transfer me and the whole discussion starts again (hours wasted on multiple days). And the message service is similar (today 2.5 hours, 5 different people, similar yesterday).

Now it seems the account has been closed which means I cannot access lots of the information online. 

To raise a dispute, I need to write to VM, and it will take 8 weeks before the Ombudsman will get involved unless VM confirm we're deadlocked - and of course VM want to be paid by Direct Debit which is due in a week (and I cannot afford to pay them 1000 - especially for something which I am strongly disputing). 

It seems crazy that I need to send VM a letter to complain, and that there is apparently no one via the customer services team who is able to receive and review an email which so clearly states there would be no early disconnection charge. 

If anyone can offer any advice or assistance I'd be so grateful.