British guns are all subjected to proof to see if they can withstand two charges in each barrel that are 25% higher than the maximum service pressure of CIP commercially produced ammo (which typically has a 15 - 20% margin of safety built in.

The thinnest safe barrel depends on what it is made from. Good steel will hold up better than poor quality steel of the same thickness etc.

If the gun is in proof and you use the right ammo, it will be fine.

I have seen guns made by the best British makers as lightweight 12-bores with original barrel minimums of 18 thou.

We in the Trade usually consider 20 thou a minimum for commercial purposes, which is why you see so many thin walled gun in auctions.

I have seen guns with damascus barres pass proof with a minimum of 7 thou.

I have also seen guns with thicker barrels fail proof.

Uniformly thin barrels will hold up better than thick barrels with steep gradients to thin spots.

There is no minimum wall thickness for proof testing. If the barrel withstands the test without material change, it will pass.