If you go with homeplugs the short answer is: fit a filtered faceplate on the master (Mk3 faceplate if's a NTE5A master) and just connect your router's adsl lead to the faceplate's RJ45 socket. No need to touch the extension wiring connections on the outer plate, although personally I would also disconnect the bell wires from the extensions if they are not needed.
Edit: sorry forgot to look at your picture, it does look like a NTE5A master and perhaps rather close to a mains 13amp socket. The proximity of the mains 13 amp socket shouldn't be a potential problem if you get the voice extensions filtered.
Edited by 4M2 (Wed 06-Sep-17 20:03:32)