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Thank you all for your help, it's much appreciated indeed.
It was my error referring to the CB's as 6V and 16V to start with.
They are indeed MTN 106 B6 (6 amps) for lighting and MTN 116 B16 (16 amps) for the twin socket.
The three core SWA cable, on the right supplies the power. I reconnected this as I could easily see that the black had been earth, brown live and grey neutral. As soon as this was reconnected along with the 16amp CB to the twin socket, it worked.
I'm sure the purpose of the 4 core swa cable is to take the power to the house switches then back again to the lights.
My problem lies with the switching to the 2 pole switch within the house, and reconnecting that from the shed end.
There was a twin joining terminal block inside the shed mini-consumer unit but the wires were torn from that when damaged.
Inside the house, both SWA cables enter below a 17th edition consumer unit and have their own CB there. They are terminated and led directly up to the twin light switch in the hall from there by the grey cable seen in the photo of the light switch.
I also think that the steel braiding around the armoured cable acts as an earth, when clamped to the steel mini-consumer unit in the shed. but there is also a separate yellow/green earth wire available, which was also snapped when damaged.
Belts and braces are fine by me though, if this is the case.
The suggestion of using 4 core swa cable, as no 3 core available is also a good call, meaning one would be dormant (unused).
There was no junction box, apart from one outside, where the bulkhead light was attached to its supply cable.