As far as I am aware the British Proof houses do not measure wall thicknesses. They take the view that if the tube does not bulge, rivel or burst when fired with a Proof load it is strong enough.

A weakness of that approach is that whilst a barrel goes out of Proof is the bore is enlarged over 10 thou, it still appears to be in proof if under that bore size even if it is repeatedly and over enthusiastically struck down, polished and re-blacked no matter how close the external diameter is approaching the internal diameter.

Some European Proof Houses stamp the weight of the barrels at Proof, and I believe those barrels will go out of proof if they suffer a certain percentage loss in weight.