A family of Microsoft relational database management systems designed for ease of use.
Okay I have Access working again thanks to one of the suggestions above although I am not sure of how it leaves me placed in the longer term.
As others have noted, the issue may be that the InprocServer32 registry entry for various classes are expecting ACEOLEDB.DLL to be in "c:\Program Files\Common Files\Microsoft Shared\OFFICE16\ACEOLEDB.DLL".
However ACEOLEDB.DLL & the rest of the access database dlls are actually located at "C:\Program Files\Microsoft Office\root\VFS\ProgramFilesCommonX64\Microsoft Shared\OFFICE16" on my system with 64 bit office installed. The Access database engine files located here are dated 2 March 2018 and are version 16.0.9029.2054. These are from the recent automatic update.
So given the apparent mismatch between the registry entries and actual files thanks to the update, I could have, as some suggested, edited the registry entries so they point to the actual database engine file location now. But I worry if that will have some unintended consequences elsewhere.
So I downloaded and installed the 64 bit Access database engine from the link given by another user above. Oila! Access now works. The registry entries are unchanged but there is now a copy of the Access database engine in the expected location (c:\Program Files\Common Files\Microsoft Shared\OFFICE16). So I can work again, hurrah.
BUT the version of the files located in this spot and presumably being used are an older version dated 7 March 2017 16.0.4492.1000.
So now my concern is, that I seem to be using a copy of Access which mixes together program files from different versions: some from March 2017 and probably some from March 2018. Is this likely to introduce problems or incompatibilities? How will it interact with future automatic updates to Access?
I have to say that I am incredibly disappointed with Microsoft about this issue.
I remember when they introduced a bug into an automatic update of Access back in the first week of March 2016* which broke the program for every user worldwide that received automatic updates. Back then, they were very apologetic, fixed it quickly and vowed it would not happen again. Not only has it happened again but this time they seem to be very lax in their response. Rather than having improved their quality control and approach, it seems to have gone considerably downhill.
* is it just a coincidence that Microsoft keep breaking Access in the first week of March or do their testing and quality assurance people all go on holidays then?