Ubuntu 18.04 failed to resolve VPN DNS when select "Use this connection only for resources on this network"

I found the following.

When ticking the "Use this connection only for resources on this network" I had no DNS as per the question.

If it was unticked, I had a duplicate default route, which once deleted, everything including DNS would work.

Comparing the output of systemd-resolve --status of these two scenarios I found the following:

When DNS worked but the options created the duplicate route, it would show this:

      DNS Domain: ~.
                  corporate-network.local

When DNS didn't work, it would show this:

      DNS Domain: corporate-network.local

The solution, therefore, is to tick the "Use this connection only for resources on this network" box and to enter ~. as an additional DNS domain.

Now the connection works directly from the network manager without having to delete the spurious default gateway and all the internal DNS resolves.