I'd go with boguing's fix - but I'd have a look at sneaky possibilities to pull a Cat 5 wire first. My youthful amateur radio experience made me a dab hand at running cables where folks least expect it...
A telephone-and-Cat5 pattress plate on the upstairs wall would look quite neat.
The landline telephone will, these days, work happily with just two wires - you need another "master socket" if you want the upstairs one to ring. Just connect the two wires to pins 2 and 5 in the upstairs and downstairs phone sockets.