My guess without looking up the figures and doing the maths myself is that if it's legit it's probably down to still being able meet disconnection times based on a very low Ze? I'm assuming it's a 90C+ rated cable type.
 
Seems a long run,& on 80 amps.
Wonder what the actual design current is.
Some cable types on the right method are comfortably into three figures on 16mm so it's not impossible (but I'll grant you unlikely!)
 
Sound like someone just looked at the fuse and current-carrying capacity and nievely said "yes gov, that will do".

Plugging in 80A, 125m and a generous 5% drop in to the Doncaster cable calculator suggests 50mm cable...
 
Maybe they don't need 80A, but I really doubt that fuse would meet Zs disconnection at that length. Also if they only needed, say, 40A or so then fusing down to that (or just above) would achieve selectivity with the (presumably) 100A cut-out supply fuse.
 

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bill01803

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Sub main 125m in16mm with 80A 1361 over current device
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UK Electrical Forum
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