JWD: Recently it was rumoured that the London Proof House was double proof testing all guns but I never heard this as definitive and I believe that this has passed into history.
As regards lapping done after proof testing, this is why there is a 0.008-0.011" maximum proof range. However, if a barrel was proofed exactly on 0.728" it could be lapped out to 0.739 before being out of proof. Obviously in a barrel with MWT of perhaps 0.020" at 0.728" this would be a very thin wall at 0.739", 0.015"!
As regards pitting, the Proof House likes to see clean tubes but will Proof test a pitted barrel providing there are no substantial pits in the area between the ribs. Equally likely to cause a refusal at the initial view are rivelling, dents and bulges and these can be almost invisible. Rivelling and bulging caused by the proof test invariably cause the gun to be failed and a subsequent retest required after the barrel has been repaired.
On the matter of wall thickness, as we are specifically banned by law from exporting guns for any purpose (including wall hangers) that are out of proof, on the request of the owners I have successfully proofed guns down to the low teens. For obvious reasons, these barrels were not worked on after proof, all the lapping etc was done before.