art-pThe OP mentioned lighting, so 7.92 voltage drop (4%) would not be acceptable if the design current was as high as 50A (so 16mm² cable would be needed) - but I wonder whether the OP's 'just a few sockets' is really going to represent a demand of anything like 50A. It would require some pretty serious machinery to be plugged into those sockets for it to be anything like that high - and, if it really were, careful thought would have to be given to how the sockets were to be configured, and what cable size was going to be used (presumably more than one circuit for that high a demand).
But would you not design the circuit in a manner that the circuit between house CU and shed CU was a power circuit.
If I understand correctly what you're saying, I'm afraid it doesn't work like that. The maximum permissible voltage drop of 3% for lighting is measured from the origin of the main installation to the light, regardless of what sub-mains or distribution cables might be in between - otherwise one could always cheat with VDs by scattering CUs all around a building and 'resetting' one's VD calculation to the physically nearest baseline!
Yes, as you say, that would do. However, as I said, if it were me, I think I'd use 16mm² SWA (only about 25% more expensive than 10mm²) - to cater for any 'future requirements' (I don't like digging!). I also would probably give very serious consideration to running it as a sub-main (e.g. install a small additional CU) rather than taking it off the main CU.
If you need to find a tradesperson to get your job done, please try our local search below, or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Are you a trade or supplier? You can create your listing free at DIYnot Local
