In the UK, pull the socket front off and look what the wires actually are. I have seen electricians use cat 5 to carry phone lines several times. It is a mixture between having cat5 already in stock, and future proofing I think. If it is cat 5 then just put an RJ45 socket on it. As others have said, you can also try running ethernet on a phone line, you might not get gigabit, but you might get more than what is comin…
I'm not convinced socket A can talk to socket B when, for example, socket B is in an extension, or... or...