I have a metal garage 16 x 8 aluminium clad on angle iron and a wooden shed 8 x 6.
First problem: Extraneous conductive parts.
The electrics installed consists of one spare run of 13amp house wiring cable
What size? 1.0mm, 1.5mm, 2.5mm, 4mm, 6mm, 10mm, or 16mm?
supplying 1 double socket in each building.
How does the cable travel between the buildings? Is it overhead? Underground? How is it protected from UV? How is it protected from physical impact?
5 amp lighting cable also supplies two lights.
Is there any fusing for this lighting supply? I'm guessing by "5 amp lighting cable" you mean 1.0mm² twin and earth.
The supply point is from a kitchen 13amp double socket of which one section has been used to accommodate a hard wired connection with neon (on) indication similar to storage heater sockets that have an on/off switch.
I gather from this outburst that you have a fused connection unit
next to a socket
They did something right then by supplying from a 13 amp fuse.
What rcd trip device can be fitted at the kitchen supply point.
There's much more to it than this.
The wiring is not encased in electrical cladding or conduit inside these outdoor buildings.
Electrical cladding???? You have no idea what images are running through my head right now.
The wiring is protected inside plastic coated metal conduit from the kitchen to the garage and covered with 2" inches of concrete.
Plastic coated metal? Please take a photo of this, because I've never heard of this.
I also suggest if you require any more assistance, you take photographs of the installation and put them in an album here (when you make a post, click "upload new images"), so we can see exactly what you are talking about. Please include a picture of your main fusebox and the box between the meter and the incoming cable.