The billing period ( bill production run ) and your individual contractual dates are unlikely to align so receiving a bill for days after you stop being a customer is normal , and any paid for dates after the served notice period are refunded, but in your case this notice period is unclear,.
You haven’t used the normal migration process ( where you advise the new ISP and they serve notice on your behalf so you don’t speak to the old provider yourself ) the actual last paid for day of your BT service includes the notice period which is 30 days after you advise them of your intention to leave yourself , but that would mean the new ISP would have to wait until your cease order is completed before they can takeover ( not migrate ) the ‘line’ , stoat means a break in service between the old and new service but that doesn’t seem to have happened, so it’s if any notice served by you has been acknowledged, I suspect your new ISP even though it’s not in your name has controlled this , so you were not ceased and re provided but migrated.
You disconnecting the equipment has no bearing on your contractual obligations, you pay for days of the notice period ( 30 days if your call was the notice to quit , or 10-14 if your Mrs migration order was used ) , what you don’t know is when this period started and ended , but it’s too early to be concerned as you may well get a refund of the majority of your last payment anyway .
