"Isn't that how it's done?"
Er, sorry Jim, but not according to P.107 of Wirnsberger "Standard Directory of Proof marks".
The "Not English Make" was to be marked on foreign-made barrels proofed in England. And foreign-made guns imported into England would have to be proofed before they could enter the English market***. I.e. proof on entry, otherwise any old junk could be imported and put onto the English market.
"You know about the proofing that takes place before a firearm can be exported from the UK".
Sorry, I don't. Proofing only if the gun was exported would make nonsense of the basic concept of British proofs to protect users in Britain.
"The second set of proofs..." There is no second set. There is only one set of recognized proof marks - the British civilian proof in combination with the "Not English Make" as required by the Rules of Proof of 1925. Any Winchester factory proofs, not being recognized by the English proof house, would be regarded as no more than inspection marks applied by the manufacturer, not recognized proof marks.
Anyway, what has that to do with "Guns for Britain", Dunkirk etc? I just do not see any connection being demonstrated by those proof marks. I see just an unusual gun that was imported post-1925 and proofed and marked in accordance with the Rules of Proof applying at the time.
We are often reminded to "buy the gun, not the story" and I feel that this is such a case.
*** "The first marking of "Not English Make" is done when it comes to UK for service" ??? Source???