Okaaay!
Seems it was me all along, and nothing to do with the problem(s) noted in this thread. When I got the Gmail security alert today, I seem to have told Google to block access from 'less secure apps' - forgot I did that. In checking Google security settings now, I noted that switch was set and so I unset it to allow 'less secure apps' access. Mail now working fine. So Google classifies Apple Mail app as a 'less secure app'!! Which means I have to allow access to ALL 'less secure apps' in order to use Apple Mail app (which I mainly use to ensure I have an offline copy / backup of all my mail and am not dependent solely on Gmail.)
Off to have a word with Google re this. Apologies for distraction from the topic at hand, but others may wish to note this, re use of Gmail and Apple Mail.