The error I received was unhelpful.
Unable to connect to libvirt.
Cannot recv data: Value too large for defined data type
Verify that the 'libvirtd' daemon is running
on the remote host.
I was pretty sure that the problem was not with the server running libvirtd because it had been working the day before and was unchanged since then. On the other hand my LMDE install was completely fresh.
To cut the chase I don't know what the fix is (it seems to be a bug).
If you read to the end of that bug thread it seems you can work around the problem by using the hostname instead of its FQDN.
For this to work of course you need to be able to resolve the target IP address using just the hostname. Since I was on the same domain as the libvirt server this was simply a matter of defining the domain in /etc/resolv.conf on the client.
If that is not a practical solution (because your client and server on different domains) I reckon you could probably configure the server hostname as an individual entry in your /etc/hosts file too, although I have not tried that. Let me know in the comments if that works for you!