I am a full (domestic) user of BT Services, including email and broadband. I also use Nord VPN. BT (and only BT) has always excluded me from logging on e-mail via BT Mail if my VPN is enabled, on my phone or PC. (I normally link to a UK based Nord VPN server). I use Blue Mail on my Android mobile phone. As soon as I am logged in to the Mail server, and re-apply my VPN services, my link through to BT Mail continues, although I note that if I stay logged in for a matter of days I can then be cut-off again, if my VPN is maintained. I suspect that happens during an automatic re-validation. I get the same issue on my mobile phone when using both Gmail and BT Mail (which I keep as back-ups) to access my BT mailbox. As it is the logging on process which exposes my user name and password this is something I would particularly like to protect using a VPN, and it is this which BT Mail Sever is exposing by its non-acceptance of a VPN as an access point. Nord VPN has a very good reputation and if BT is blocking its servers it is doing so without basis.
On my PC, so far, I have found that Thunderbird is not locked out of the BT Mail server, even when my VPN is active - I suspect that Thunderbird accepts Nord VPN as legitimate, and the BT Mail server accepts Thunderbird. This doesn't seem to apply in the mobile sphere.
As VPN usage increases (for a variety of reasons, not least for security) I don't think BT Mail's dislike of VPNs is really sustainable. It would be a good if a BT Mail expert could comment. I appreciate the help gained from non-BT official people's advice, but this seems a policy issue outwith their 'work-around' expertise.
The message I get from BT (on a PC) when I try to log in with VPN enabled is - Sorry we couldn't connect you. If you continue to experience issues, Please contact BT and quote Error Code: TS-0003. Details to Contact BT
