PROBLEM SOLVED!!!
I realised what you meant, so I tried a new user account, which was able to access Mail, although my original account wasn't.
The problem was in Preferences. I have far too many, because our ISP has been transferred from telco to telco to telco.... sometimes with no problems, sometimes disappearing for a while. i've restarted from scratch a few times! At least we have kept our email addresses. Somehow the Preference was changed: it must have been me, but I don't remember. Probably shutting down without paying attention.
However, I'm now reconnected.
Many thanks for your help.
Steve