Solved - Error Code 0x80240031.
After spending over a week trying to solve this error and following the many suggestions kindly offered by numerous contributors on this and other forums, I still could not resolve this error and download the anniversary update.
The problem was isolated to one PC (which had already successfully upgraded from WIn 7 to Win 10, so the hardware and software were OK). All other eight PCs on the LAN network installed the anniversary update successfully.
The solution which worked for me, was in the end, very simply (as it usually is). Under 'Settings/Update & Security/Advanced Options/Choose how updates are delivered', I had 'Updates from more than one place' turned on and 'PCs on my local network' selected - as is the case for all PCs on the LAN. Going back to basics and given that it was only one PC that was not upgrading, I thought there may be something slightly different with this PC even though it had successfully upgraded from Win 7. In the end, I simply turned off the 'Updates from more than one place', thereby forcing the PC to download a fresh copy of the anniversary update, rather than using the copy from one of the other PCs on the LAN.
The update took a while and at first there appeared to be no activity (for about twenty minutes). Be patient, it took over an hour to download and install. However it successfully installed the anniversary update.
I appreciate this solution may not be for everyone, but I suggest you try this first as it does not involve any of the very complicated and time consuming solutions suggested by Microsoft (on other forums) - none of which seemed to solve the issue for users. This solution simply requires the deactivation of one feature.
I hope this helps others having the same problem.