I downloaded the new version and tried running it (instead of using the 'Check for Updates' button inside the application, which always appeared to do nothing). The installer failed, recommending that 2GB free space was needed. After a couple of iterations, I had eventually freed-up disk space to be ~5GB.
Running the installer this time led to a 'successful installation' and after rebooting the computer, the system tray icon still reported 'Your are unprotected!'.
I did nothing more than rebooting the computer 2 more times and upon restarting, THIS time the tooltip on the system tray icon showed 'You are protected'. I also checked the 'defs' directory and there were only a couple of 'today's date'-directories in there, instead of the 100+ directories that were there previously.
Getting back into the GUI for the application, it showed the Definitions were Ok.. but I clicked the "Check for updates" button (for the Virus Definitions) and again it shows the 'release time' for the updates was the most recent time I clicked the 'Check for updates' button.. so maybe the wording of the message is incorrect... or there's still something wrong...
...but the behaviour of the application is now the same as it has been for the last few years.
Many thanks to everyone for your help.