Rather than running VDSL from an extension socket you could do what I've done. My home has cat5e cabling in most rooms in the house, which all terminate at a patch panel in the garage. There's an RJ45 socket beside my BT master socket, so I've plugged the VDSL cable (it's an RJ11 cable?) coming out of the master socket into the adjacent RJ45 socket, and from there I've patched that connection to another RJ45 socket in another room, into which the fibre modem is plugged and connected to my cable wifi router. It all works perfectly with no drop in speed.
You could do something similar by installing an RJ45 socket next to your master socket, run a length of cat5e solid core cable from that to another room where you want to locate your router, and terminate the cable at another RJ45 socket, into which you can plug your modem/router using another RJ11 lead. The RJ11 plug will fit the RJ45 socket but it needs care and leaves the unused RJ45 pins exposed, so what I've done is cut an ADSL/VDSL cable in half and fitted RJ45 plugs at the exposed ends, but I now see that you can buy one of these
to do the job.