So, after claiming in a previous post that I was a master at connecting Mac/OSX Mail to Exim, it stopped working again. Looks like I had a brief period of working, and then it stopped again.
The Mail connection doctor was not helpful at all, it took me a while to work out that it was timing out, so that after any test I needed to go away for 5-10 minutes, wait for the time out, change another setting, then try again.
The result of all that was to change the following setting, which on my install is in /etc/exim4/exim4.localmacros.conf:
gnutls_require_protocols = TLS1.0:SSL3
That seems to have it all going.