Well, I went out for a while and left it..but an hour and a quarter after I first rebooted it was still claiming to be doing update no. 3 out of 18, so I power-cycled the PC.
It booted up with a "Configuring Windows updates" message at first, followed by an automatic reboot. Everything now seems to be back to normal, and my browser is responsive again.
The only minor concern is that Windows is now, of course, wanting to install the updates it didn't install in the first place (in my shutdown options). So I might leave that for a little while to see if anyone else has problems, or whether the failed installation was down to some bit of software on my PC disappearing up its own arse. The fact that I had an issue with my browser before the original update might indicate it was a problem at my end, which manifested itself as an unresponsive application and update non-installation..
I'll report back when I get the bottle up to try it.
EDIT: Rebooted - the other fifteen updates installed ok, Windows configured itself and everything running as required in about 6 mins. So it looks like the problem was at my end.
Last edited by Blues&twos; 15th November 2014 at 12:27.