Okay I managed to get just one of the accounts working with secure settings almost accidentally, by doing the following:

For the heck of it, I tried setting the 'Use encryption type...' to 'Auto' in More Settings -> Advanced, and I got a dialogue "The server you are connected to is using a security certificate that cannot be verified. The target principal name is incorrect"

So I viewed the certificate, whose status showed OK, and with an option to install it. So I went through that process, got a success message, OK'ed out of everything, and tried to set the account up with secure settings- and bingo, it worked!

My joy was short lived as none of the other accounts responded in the same way, and now I get the same certificate verify dialogue every time I start Outlook- although I can click 'Yes' to 'Continue using this server?' and the one account with secure settings still works.

The target principal name on the certificate is *.f-------s.net, which is OK for the server concerned which is within that domain. I am naming the server in the Outlook settings. Googling the certificate error does however suggest a mismatch in the settings- but everything appears correct, ports are correct- I'm using 993 IMAP and 465 SMTP for SSL/TLS.

In any case, such a mistake would not explain why it suddenly stopped working when my other devices and computers continue to work just fine?

I still think I'm on the right track with SSL and Certificates as the cause...

Alan