Obviously without knowing the exact conversation you had , and if the advisor fully appreciated what you were trying to achieve, who knows what happened, but AFAIK, 30 days notice is more a billing requirement rather than necessarily a service end date , if someone asked for their services to be ceased immediately, they would be billed for the 30 days because that’s what the T&C s stipulate, you would think that service would continue during those 30 days , but maybe not, perhaps the language used may be key, your requirements were more involved that simply saying , here is my 30 day notice to quit .
Pure speculation , but if you said cease my broadband today and assumed it would continue for 30 days , that may not be the case , with FTTC ( assuming it’s FTTC you had ) it should continue to work irrespective of the physical status of your PSTN ‘line’ ,( ceased , stopped , stopped /renumbered, etc but ceasing OSTN does trigger the cessation of broadband ) so presumably the broadband was programmed to be ceased on the day you called ( well the day after so it works until at least midnight ) or coincidentally there was a waiting customer on the FTTC cabinet, and as soon as your FTTC port was deemed ‘spare’ it was allocated to another ISP customer and the connection physically moved to service a different address , or even your BT Broadband account was suspended pending cessation, so your connection FTTC remained in tact but your account effectively blocked from internet access , the status of the router would be informative here.
Its impossible to know for sure , sage advice for anyone moving network providers, where keeping internet access important, is only once the new network is in and working, cease the old network, even at the cost of paying for both for a period, as you say , luckily your new provider gave you a month free anyway.
