Same problem here on an HP Probook laptop. You might be able to reset your phone / e-mail details for passcodes by following:
MyBT > Your Details > Profile> Edit Contact Details
and then use the purple link 'Go to 2-step authentication'
This shows the phone number / e-mail address for 'Where should we send your passcodes' but it seems to relate to recovery messages, not 2FA, as per the headings, which is inconsistent with the wording of the link. Proceed at your own risk? I did not dare to try changing anything to avoid a lock-out but it looked to be active. The BT system even sent me a 4 digit PIN via a text message as I exited this page (Note: the 2FA code is normally 8 digits if I remember correctly, might be 6) but this did not reset the 2FA to make it work properly. Something is inconsistent / really fouled up.
I went looking for this because my 2-factor / 2-step authentication has failed on my BT log-in so my BT account and BT e-mail load straight from entering the password without a 2FA code which I consider to be a serious security vulnerability. Note: 2FA is still working on my other on-line accounts.
The BT system says the 2-step authentication is 'ON'. When I click on the link to get to the edit page the phone number and e-mail address are immediately covered up with a purple BT banner full of BT links and a red warning "Sorry, we couldn't save your changes. Please try again.' Surprise - the 'Try again' button does not work.
I have tried Edge and Chrome. I am not using a VPN on this machine. I used C-Cleaner and the Chrome's own functions to wipe cookies, shut everything else down, turned off a GDPR consent [NOT] auto-fill extension in Chrome, rebooted my PC, adjusted the screen zoom to make sure that it is not simply a screen zoom overlay error, etc. I also had the same access direct from password problem on another PC so it seems unlikely that it is my machine.
I tried the BT on-line chat / techs but they were unable to suggest anything other than adding BT mail as an option in Outlook. What? Whatever ... same result in Outlook and it did not cure the BT vulnerability.
I tried to raise a complaint because this looks like a systemic vulnerability (which might affect other people who might be blissfully unaware) but - surprise - "There seems to be a network issue" so I was unable to do so.
Only option for me seems to be to go through all of my on-line accounts / resources that are using my BT e-mail as a back-up, change to something else and abandon the BT e-mail before it gets hacked.
