The Varnish service was starting OK but it wasn't using any of the parameters, set in /etc/default/varnish.
For example, set the
listening port to be 80, but Varnish would always start with port 6081.
The Varnish service (/lib/systemd/system/varnish.service) wasn't using
any parameter files - instead it was hard coded to start with the
default values only.
The temporary fix is to edit the varnish.service file and manually configure the parameters to match your needs.