In the error message (attached below) the open_basedir value is shown as
/var/www/html/:/tmp
while Joomla! System Info shows the value as
/home/myusername/:/tmp/:/var/www/html/
The reference to the base of my shared hosting appears to be missing in the error message triggered by backup.php.
Folowing is the full error message provided by cron ##text##
David