Just out of curiosity, why SWA for wiring the sockets?
How to you terminate the armour?
If it is 6mm then you will have fun putting 2 of them into each socket.
It would depend upon the make, but 6mm would be the limit for termination in box and terminals
 
Run a suitably sized sub main, in a roughly central position in the stadium, fit a suitably sized distribution board and wire your radials/RFC s from there, still can't understand why you are saying the sub main will need to be sized there and back.
 
a 25mm SWA is needed, which obviously inst viable for a few sockets.

Why not, I once installed a 35sq cable for 1No 13A double socket (Fridge and kettle) to a fishing/hunting lodge over approx. 200m.
The owner thought less hassle than continually getting fuel for a generator! So eventually paid for itself.
 
Possibly run more than 1 sub circuit. 3 phase or 1 phase Sub circuits to be suitably sized for known load plus spare capacity for unknown (with -in reason) load. I would keep all the final sub circuits to a sensible distance. Possibly use 16 amp sockets for caterers to plug into. As mentioned before, I would get a spec to say to what is required. You may leave yourself wide open later on being sued, if not adequately designed.
 
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Title
Calculating Cable Size for Ring Circuit
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Electrical Wiring, Theories and Regulations
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appspark,
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