Right, as an experiment before doing the shutdown shortcut I tried using 'shutdown /s /t 5' from a command prompt window.Here's what happened, if anyone's still interested!
1) Got Windows message 'Windows will shut down in less than 1 minute', then everthing froze for about 60 sec.
2) Then the desktop disappeared and the screen went black for about 3 mins.
3) Then the desktop reappeared for few seconds, followed by the normal Windows 'Logging off' screen with the spinning circle.
4) Logging off only took a few seconds, followed by a normal shutdown a few seconds later.
This just gets more random by the day! Hopefully by the end of the week it'll run out of bizarre stuff to do and will give in and start working properly again.