Thank you, Norm, for your suggestion.
I already had a look at this article, but it is not very helpful.
Under the heading:
"Unable to Backup - An error occurred while copying files to backup volume" - which is what shows up on my screen, the advise is:
"Restart - then try the backup again"
Regrettably it doesn't say what to do when the restart and retry still doesn't produce a backup!
I have no idea what to do to have Time Machine backup again?