Here's another twist on this problem.
I have set up ADSL on my parents' PC - this is on a working phone installation with 5 extensions. The Broadband MODEM is plugged into the master socket.
The MODEM diagnostics confirm the problem that we see - it sees a broadband signal if we disconnect all of the other extensions (by removing the faceplate that you mention) and, after disconnecting the wiring at all of the other sockets, will work if we add just one extension. When I even just connect open-ended wires to connect towards the next extension, the BB signal instantly drops out. I have tried a simple resistance check across the onward-cabling and there does not seem to be an issue.
Any ideas please ?