Andrew wrote:
I have a mains socket in my kitchen that seems to have been added as a
spur (the cable is a different colour ro all the other sockets). The
cable goes through the inner leaf of the cavity wall, travels
horizontally for approx 18" and then comes out of the cavity and is
wired into another socket.

How did someone manage that?
They could've used a special cable pulling kit.
I've managed with straightened wire coat hanger or flexible plastic strip
e.g. capping off plastic conduit or curtain rail.

More seriously, tha cavity insulation appears to be small polystyrene
beads. ISTR reading in a previous post that polystyrene and mains
cable are incompatible. Should I re-route the cable whilst replacing
the kitchen?

Andrew