After doing that, I restarted the box and got the Mint login screen, entered my password and got . . . . . a black screen with a mouse pointer and nothing else.
I couldn't find an answer on the Internet so eventually I took a punt and entered:
apt-get install cinnamon
and what would you know, Cinnamon wasn't installed at all. For some, the distribution upgrade had decided to remove Cinnamon altogether. After the install finished I rebooted and all was good again.