There is a lot more to consider than the size of the wire.
The siae and type if wire will depend on ( among other things ) Length of cable, how much load ( 32 amp is abput 8 kW of power ), how will cable be installed.
Insulation testing, loop reistance checking to ensure safety devices operate quickly enough in fault conditions.
You probably do not need a fuse box at all for just one light and a couple of sockets.
RCD protection, yes. But you probably have that at the house end already. From where do you plan to feed this aerial cable?
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