Relocating the master socket wouldn't make any difference, even if you were allowed to do that - which you aren't.
What you could do, if the cable you have from it to your extension is decent phone wiring, (CW1308 is the normal), is replace it with CAT5 beforehand and connect that to an interstitial faceplate shown in MrSaffron's two links. You are allowed to add and remove stuff to/from the back of the faceplate, and fit that intermediate one.
You wouldn't need anything connected to the faceplate then, unless you have some other extensions currently connected to it. Note that you would be connecting the CAT5 to the A/B terminals pointed to by the yellow arrow.
Unfortunately it is a bit bulky. Sticks out rather more than at the moment.
Edit: Thinking about it, it would be unlikely to make much difference if you forget about the interstitial plate and just connect the Cat 5 to the back of the faceplate instead of the existing cabling. I'm assuming you don't want a phone there.
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Edited by RobertoS (Tue 30-Aug-16 17:23:39)