Sky don't do the work BT do.
and yes you need a new socket face.
It's a completely different face so you have no choice for it to be changed.
Well guess BT will have to sort it then. It's the old type socket, that has small wires coming from it, that go to a junction box (I can't remember the actual name), that has the telephone cable coming in from outside and attaching to that.
There's pretty much no slack on it though, just a tiny run of cable, then the box, then a longer run of the smaller cable. The new socket will end up pretty high up the wall, if it even fits, as the little junction box thing is right under the window, so might not be room there for a proper socket.
Chances of them doing a new cable from the telephone pole? As the whole lot is pretty old and tatty (doesn't seem to effect anything), the actual cable between the house and telephone pole is twisted as well.