If Vodafone installed a ‘new fibre line’ presumably this is FTTP , so is it over City Fibre or Openreach , and did you have a telephone service with BT and you asked Vodafone to port the number ( so VF are providing the same phone number ) ?, on what are you basing your BT service still being ‘active ‘ if you have sent the router back presumably it’s not because it’s still ‘working’ ?
If your BT service was acknowledged as ending in the 11th of October then it’s probably a bit early to be overly concerned , it’s quite normal to be charged for some days after the ending of service and then refunded for those days , as the billing cycle won’t align with the date your notice period ended ,obviously after that bill reconciliation is done , if you don’t receive a refund for 12th October onwards then you have a valid complaint.
FWIW , if you did take telephony from VF and they didn’t request the phone number be ported in a timely fashion ( basically requesting it after 10th October ) that could impact the actual date your service ‘ends’ with BT , plus who gave notice , you directly by calling BT , or by Vodafone using the new OTS ( one touch switching ) platform ?
As you have emails acknowledging the 11th as your last day with BT , if your ‘BT’ line and broadband appear to still be working just because the account is accessible on line ( presumably that’s why you are concerned ) , ultimately its of no consequence to you unless you eventually ( after the paying and refunding cycle completes ) you pay BT for those days , and it’s too soon to know that .
