I doubt if it would be BT stopping your use of a VPN to get your mail, it is more likely to be the way VPN's work. Otherwise you couldn't use a VPN setup as a P2P connection, which allows you to get your mail.
Perhaps we should stop blaming companies because we are not able to sort a problem, which would appear to be due to our own shortcomings. If you want to use a software program you would really need to do some studying, to understand how it works, otherwise you could tend to make mistakes, blaming it on the software rather on ones ability to understand it.
One went to school to learn the basics of education. Now we have computers, we should learn to use them correctly, schooling.
I think using the P2P setting simply puts the traffic through a different server that is better setup for P2P and probably thus uses a different IP address. You can check this by using the P2P setting and checking your IP address, then without and see if its different.
I suspect the mail servers drop connections based on IP addresses as said before. If your theory was to be correct we would be unable to connect through any countries, but we can, some work, some don't. POP3 (email) is somewhat simplistic in its protocol so I think the servers block/drop traffic from servers on blacklists somewhere.
I don't understand how this is our shortcomings, if it is filtered/blocked/dropped at the email server end, how can we fix it and sort the problem?
Could this not be because the IP addresses of the P2P VPN servers have not been blacklisted by BT like the other VPN servers because they are mostly used for torrenting not email ?
You sound like you know what you are talking about and I'm no expert so could you kindly explain why you think a VPN configuration might effect connection to a POP3 server ?