So he just isolated the socket by tripping the fuse at the C/Unit.
So that socket is the only one on that circuit?
Is it a radial? What cable size and device rating?
As its rented accomodation and we can do whatever to the house (checked with the landlord)....
I would be gobsmacked if "do whatever to the house" included dangerous electrical work.
Or work which was illegal, but I don't know what the law in Scotland says.
is there any easy fix for this.
As when you take the socket off the wall theres the L N and E cable there.??
You need to check that they are actually connected by doing continuity tests.
You then need to measure the earth fault loop impedance at the socket, add on the expected R1+R2 for the cable to the shed and the cables there to check that it
will be safe before you start.
You then need to find a way to join the cable at that switch to armoured cable which you run in a
trench to the shed and join it there to the cables in the shed. The easiest way would probably be to put a waterproof enclosure on the outside of the house, CW gland on the bottom, SWA cores through the wall and crimped onto the internal cable. Same idea at the shed end.
You'll need to use a banjo or earth nut on the glands to ensure the armour is earthed.
See the Wiki article on working with SWA.
Then when it's done you need to do continuity, insulation resistance, polarity and fault-loop tests at the shed.
So yes - reasonably easy if you're competent.