Brother MFC-J6720DW "not connected" to MacBook Pro
OK, it's working again but I'm puzzled how I achieved it.

I turned off the Wi-Fi on my MacBook to confirm that the connexion to the printer was definitely only via the ethernet cable, and after I turned it on again I saw "MFC-J6720DW multifunction" as the name of the printer. I added that and then was able to unplug the ethernet cable and both print and scan over Wi-Fi as before. I don't know why that should have been effective because I had already done a system reset on the Mac without success in being able to use the printer over Wi-Fi.

Sorry to have wasted anyone's time!

in friendship

Rowland