It seems there was a security feature builtin to the Chrome/Edge which prevents local links (file:///c:/test.xls) to open.

This seems to be pretty awful for Intranet sites where this was used for ages, so you end up with an endless amount of local links around.

I really also don't understand why you can't define an exception for e.g. local files/Intranet. But however there are some solutions/workarounds I found.

Use Firefox

To be honest, even if the new Edge is a very cool browser, they did a lot with Firefox and I think this is a also a decent choice you should consider even for a company.

Change the Group Policy to handle a list of exceptions as "Internet Explorer"

This applies to Edge and reading through the articles this means a lot of configuration and fiddling with Group Policys.

Rewrite the links and use Office URI schemes

This is the solution I went for, of course you need to be able to change the links (which is possible at my side), and it is all about office documents here, so this fits my needs.

So the links changed from:

<a href="/ file:///x:/localintranetfiles/mytest.csv ">Download</a>

to:

<a href="/ file:///x:/localintranetfiles/mytest.csv ">Download</a>

to

<a href="ms-excel:ofv|u|file:///x:/localintranetfiles/mytest.csv">Download</a>

I hope this helps to find a proper solution for you!