I took a look at my partitions and as my laptop originally had just a 120gig SSD, the system reserved partition was less than 2 gigs. On the hunch that this might be causing the problem, I used the recommended Minitool partition wizard to extend the system reserved partition to about 25 gigs. I ran KB2919355 again, but the result was exactly the same. It seemed to install just fine within Windows and then failed after a series of reboots with the same "We couldn't complete the updates. Undoing Changes" message.
It does not look like the reserve partition size made any difference, my problem is the same as before and this update will not install.