Ok, now we just need to determine which of the 2 possibles is the master socket. If there is no dial tone at the MK3 test socket, check if there is dial tone at the test socket of the other socket you pictured. If so, plug your router in there with a filter and see what happens. You really need to use a proper tool to insert the wires as using a screwdriver or suchlike can be the cause of wires popping out as the gap has been widened.
You can get a cheap plastic one from Maplin
I thought you said yesterday you didn't get dial tone at the test socket of the MK3. The dining room doesn't have a test socket. This is the socket I meant you to check for dial tone at the test socket.
Ok, one last test. With the faceplate of the MK3 removed, there should only be dial tone at the test socket and not at any of the other sockets.
In that case we have finally managed to ascertain that the fault is external to your property and will require an engineer visit to fix.