Lewden (very industrial, art deco style, 5A 13A 15A 30A) or Clipsal
(modern knockoff).

I would bring the cable in from the rear.
Run oval or round conduit down the other side into a BESA box sunk
into the wall, rear exit the BESA into the rear of whatever you
choose. No problem feeding a tape down with magnet, snap onto a magnet
puller and pulling through - along with conventional FTE. Permits
cable replacement easily in the future. You could sink the socket/
light switch and use brass faceplates, just realise moving them
requires quite a bit of future work if you change your mind :-) For a
horizontal run do the same re two leg conduit box and chase the wall
the other side horizontally. BESA boxes work well for this kind of
stuff - same with wall lights although some require architrave if the
light fitting itself is quite narrow.

Cable running down the wall may work , but a socket/switch sat
"cleanly" on a brick wall can look much better. Consider the outside
of your house - do you prefer cables running down to an accessory or a
lone accessory & lone light on the wall? Most people prefer the latter
with the cables hidden, particularly with FP200G/BS8436 being white.