I installed the update at work - it worked. I installed the update on my old PC - it worked. Tried to install it on my current PC - failed, after taking something like 20 minutes. It then took another half-hour to revert the changes. (On those machines where it worked, it took only 5 minutes or so to install).
Digging around online showed that fiddling around on the command line with dism might help. The online image is corrupted but it's repairable... that is, until you try and use
So, after faffing around and grabbing an install.wim from an old 8.1 iso I had saved at work (not the 8.1 update 1 iso currently on the MS website) I find that dism won't use the image, even after mounting it.
I couldn't then even attempt to reinstall the update, as it failed immediately. Dism was called upon again to remove the update package, then at least it would let me try again... only to fail. Another 45 minutes wasted.
It looks as though the only way to "fix" it is to nuke Windows entirely, then go through the painful 8.0 > 8.1 > 8.1 with Media Center route. Except, of course, to get Media Center reinstalled you have to buy it again - there's no option I can see to re-enter your Meda Center key again because, guess what, when you upgrade to Media Center your Windows product key is changed. And a Windows 8.1 with Media Center key isn't accepted by the 8.1 iso (or at least wasn't when I tried earlier)...
Looks like a long and boring Easter weekend coming up.
On the other hand, I might just reinstall Windows 7 instead.