It seems replacing the master socket faceplate did the trick. I was surprised as looking at the faceplate theres't nothing there other than moving the connection vertically up internally.
The plug on the faceplate has contacts on the top and bottom of it which are connected together. The test socket also has two sets of contacts, with one set connected to the incoming line and the other connected to the cam-lock terminals. When you install the faceplate the two are connected together. This is the whole point, so that when the faceplate is removed all your internal wiring is disconnected so that Openreach can verify their own wiring without including your own (making the socket the 'demarcation point'). You can see in much more detail how the socket works here
https://www.youtube.com/watch?v=CkFMfB-DYmQ and what is inside it here
https://www.youtube.com/watch?v=jD67a-ZC7VY.
Listening to the dial tone on the extension socket gave no normal dial tone - but instead gave quiter faster higher-pitched "clicks". About 3 or 4 per second. Is this something to be worried about? We're not going to use landlines so this question really is about safety - am I burning any components?
Is this perhaps the stuttered dial tone you get to tell you someone has left a voicemail message (call 1571 to pick it up and delete it if so)? If not, I'd say this doesn't sound right. There won't be anything dangerous here that's going to cause damage, but there could be a bad connection which could end up messing up your DSL connection later if it gets worse. Call 17070, select option 2 (quiet line test) and have a listen. The line should be completely silent.
Anyway - the DSL synced at almost the master test socket rate. Modem reporting current throughput 40Mbs down and 9.2 up.. and speediest giving 37 and 8 Mbs .. which is a massive improvement. The frequency spectrum is also "full". Previously at the extensions the higher frequencies were being filtered out.
The modem also isn't reporting any "branching" which is also good.
Excellent, congratulations on your improved service. It sounds like all the bridge taps have now been eliminated. It looks like you have interleaving applied to your line (hence the 8ms delay on the downstream). If you now leave the modem connected and undisturbed, with a bit of luck, this will be removed over the coming days/weeks which should give you slightly lower latency.
THANKS EVERYONE - I think this should be listed as a real success of people helping each other. Myself, I've barely changed a lightbulb! (I do have a physics degree so I know what volts are but I've never done it practically)
You're very welcome, and I'm pleased you got a good result. I believe there's quite a few physicists here (myself included)!