I'm getting somewhere, @Rob Caplan - MSFT .
I suspected that the Published/Unpublished app base directory may make a difference and putting the following in the *.cproj file did the trick.
<PropertyGroup Condition="$(TargetFramework.Contains('-windows'))">
<AppxPackage>false</AppxPackage>
<PublishAppxPackage>false</PublishAppxPackage>
</PropertyGroup>
Now the local files load as expected (also while navigating) but with a minor issue. On start-up, there is a momentary error message as shown below (lasts about a couple of seconds) from which Webview recovers.
Having got this far, I can live with the minor issues, which hopefully will be ironed out in due course. Automatically taking care of the app base directory for published and unpublished from WebView side would be ideal. I understand this point is already under consideration.
Thank you again.