Thanks for all the replies.
To hopefully reassure everyone, the starting point is a professionally installed external 13 amp socket covered by a recent inspection certificate. So electrically all I am doing is running an extension cable.
I wired the whole house with Cat 5 about 15 years ago and could extend that but as there is an Ethernet socket next to an indoor power socket on the other side of the wall to the external socket, I'm hoping for an easy solution . I'd really like to avoid drilling even more holes in the wall.
One of the goals is to pickup weak feed signals on satellites at 7E and 10E that my motorised 85cm dish fails at. So out comes the venerable 1.2m Channel Master. A short cable run from the dish to the shed using some CT165 cable, that I already have, is going to be much better for this than running similarly thick cable from the dish to my main receiver ~40m away with significant cable loss. Fibre optic LNBs don't seem to fit my DIY requirements yet.
I'm still tempted by power-line Ethernet. If that doesn't work, I'll go armoured Cat-6 or a directional Wi-Fi antenna.