Re the attached image, I do not suspect BT of something suspicious, so what's going on with this seemingly invalid certificate. (It arises out of my trying to set up my Mozilla Thunderbird Email client to receive mail.
Can someone interpret it for me and tell me what to do?
It's hard to say without seeing the details of the certificate, but I think you're getting the error because you have T'bird configured for a SSL connection and the certificate is for pop.mail.yahoo.com, while the server that you have configured is mail.btinternet.com (which is a "front end" that directs your email traffic to Yahoo servers).
I'd guess it's the mismatch between the configured server (btinternet.com) and the certificate (yahoo.com) that T'bird is objecting to.
I thought this question of identiry theft would raise a few eyebrows—but no takers?
It's not identity theft. I also get the same message when setting up a Thunderbird email using SSL.
I agree with IanC here - and it's actually nothing to worry about.