try billing live chat and see if they can help you https://www.bt.com/help/home/contactus/public/echat/prechatsurvey.html?type=r&webreason=10007&num=98...
Was the correct process used to move to your new provider ?, if it's anyone other than Virgin, then you contact the provider you want to use and they do the rest ( it's a gaining provider led process ) , you would know it's progressing correctly as you would get a 'sorry to see you go ' type email/letter from BT.
If this is the process used and you received that notification from BT, then it may just be the changeover was close to the billing run, and you should get the money refunded ( so if you payed by direct debit, don't cancel it yet, as the refund should be via a reverse DD) ....if on the other hand either you or your provider didn't follow the correct process ( and not getting the 'sorry to see you go notice' is a clue it wasn't done correctly) then you may have got a new line from your new provider not a migration, and BT will be unaware that you have changed provider , hence the charge.
Did you port your number to the new provider and if you did, is that number on your new providers line ?, if it is then that means your BT account will be closing , if you were not bothered about the number, and got a new number from the new provider, try ringing your old number , if it 'rings out' then your BT service is effectively still live , and you will need to give notice to BT, as said , if that is the case , because it's gaining provider led, then the blame isn't with BT, but the gaining provider
Chances are that your October bill was already in the system, most (if not all) charge in advance for line rental and in arears for calls, so depending on the actual dates on your BT bill , you should pay from the 'start' date upto and including 21st September, and your new providers bill should start from 22/9/18, so any rental days on the last BT bill 22/9/18 onwards should be refunded when the final BT bill is produced, by a credit to the account your payment was taken from, that is if the line rental refund is more than any call charges, I believe BT refund automatically.