Right, it's sorted out! Oh the relief.
It was partly luck....and a bit of Mrs. B&t having a go at it too.
We waited until the "For Recovery Press F10" screen came up and then one by one pressed all the F keys, and when that didn't seem to do anything, she pressed the Windows logo key. One of these keys brought up the Windows recovery menu which included the Safe Mode option. I've heard that F8 should do it on this screen for a MESH PC but it wouldn't work when I tried it last time.
I started Windows using Safe Mode, then used System Restore to restore the PC to the most recent good system checkpoint (i.e. before we'd attempted to download the updated driver) - yesterday, as it happened.
Windows restored successfully and is now running normally again! Yes!
Bloody computers.
