As you are no doubt aware, the BT hub is a mass produced product made for the masses of BT customers to be used on the BT ISP's broadband network and the hub has limited scope for users to intervene in its settings.
This is pretty standard practice for all ISP's routers because the vast majority of customers do not wish to tamper with supplied equipment and no doubt ISPs do not want customers tampering with settings which may cause unintended issues with their broadband connection. Both parties just want it to work.
The BT hub which comes with BTWifi activated, which you now know you agreed to when you joined BT, and the BT hub does have a software "button" to turn off BTWifi. While I do not know the exact workings of this, I presume that when this is activated by a BT Broadband customer, which you have said you are not, this sends a message to the BT ISP's servers when it authenticates during normal usage on the BT Broadband system.
When this signal is received BTWifi is turned off in the software. This usually happen with 24 hours but it can take longer. There is no human intervention required to make this happen.
If the BT hub is "factory" reset, this restores the default setting to have BTWifi active.
Because you are using the BT hub on a different ISP's network, albeit that ISP is member of the BT Group, the BT hub is not sending or receiving authentication to the BT ISP's network so therefore it has no knowledge of the BT hub and can not action any request for BTWifi to be turned off.
Like others who have posted, I am surprised that although the BTWifi wireless signal is active that you can actually log onto it and use the Internet.
EDIT: Post crossed with the above. As regards the BT Terms and Conditions you referred to about turning off BTWifi. The T&Cs and their contents apply to BT Broadband Customers. As you have pointed out, you are no longer a BT Broadband customer therefore they do not apply to you or any residual BT equipment that you have chosen to use on another ISP's network.
