At the moment, my understanding is that you have the modem/router situated near the extension socket and use a microfilter to make the connection. Do you have anything connected at the NTE5 (the master socket)? If yes, is that other device also connected via a microfilter?
All of the wiring from the lower front face-plate at the NTE5 to the extension socket is your own. The extension socket is also your own. (it was given to the owner of the property when the NTE5 was installed.)
To be perfectly honest, I'm not that sure if fitting a centralised filter at the NTE5 and then running data cabling from it to the vicinity of the modem/router would achieve much.
Without physically seeing
and touching the current set-up, anything I suggest will just be a good guess.
Perhaps look in the classified advertisements of your local paper for an ex-GPO/ex-PO/ex-BT person who would be willing to visit, inspect and advise accordingly?