Well, everyone.
After more investigation I found it boiled down to me having IOBIT's "Advanced System Care" running as a service set to "Automatic".
After rebooting in Safe mode (as mentioned previously) you need to change a setting for ASC (Advanced System Care) in the "Services" module as follows:
1. Boot your machine into "Safe Mode" via the command prompt found under "Advanced Options" when you reboot from a rescue
disk (you should create one of these when you perform a "Create System Image", which everyone should do from time to time).
The commands to type at the DOS prompt are:
C:
CD C:\Windows\System32
BCDEDIT /SET {DEFAULT} BOOTSAFE NETWORK
Then click "OK" on the dialogue that appeasr to boot your machine into Safe Mode.
2. Now for ASC (Advanced System Care).
You do not have to uninstall ASC, just change its "Startup Type" under Services.
Do this by typing "Services.msc" in the Cortana search box and hitting enter.
Find the item for Advanced system care and right click on it and select "Properties".
You then change the Startup type to "Manual" and clicking "Apply".
Finally close your "Services.msc" program by clicking OK
3. Back to the "Cortana" search box!
Type in "MSCONFIG" and hit Enter
Click on the "Boot" Tab and UN-CHECK the "Safe Boot" check-box and click on Apply, then click on "OK"
(This will ensure it does not boot into "Safe" mode every time).
3. Now run "Windows Update" under "Settings" and once the update with which you are having trouble is ready to install,
reboot your machine and let the update proceed.
Interestingly, once the machine updates correctly and returns to normal, if you check "Services.msc" again, you will see that the setting has reverted back to "Automatic". This is because within ASC under "Settings/General Settings" (click its top left Hamburger
Menu) you should have "Load Automatically at Windows StartUp" checked.
The ultimate outcome of all this is that the update succeeds, and ASC runs as expected, back to its normal defaults.
Keep the thought of "Services" in mind whenever an update fails.
It may not just be ASC, but could be another service that starts running at time of boot-up.
I assume that this fix could well apply to any computer program that performs "optimization" or maintenance on a computer system.
If you do not own ASC, investigate other programs you may have running as a "Service" - they may be causing your Windows Update to fail.
Happy Days! :-)