Some misunderstanding there on British proof marks. Guns sent to England during WWII or under Lend Lease were not given those proof marks when received in the UK. Some that were actually issued were marked with the military proof and propertly mark (broad arrow) but many were not.
Those proof marks usually seen on surplus guns brought from England are post-war commercial proofs, applied when the guns were sold out of military storage. They are not "export marks", since the guns were proved without regard to their ultimate destination, nor are they US "import marks". The word "ENGLAND", on guns made in that country, is the Country-of-Origin mark required for all products imported into the U.S., and was usually put on in bond in the U.S. (The 1968 law changed the requirements for marking firearms and the COO is no longer used for surplus guns.) The COO mark was not normally applied to US made guns being brought back, though mistakes were made, like the Savage-made No. 4 rifles I have seen marked "ENGLAND".
If the British military bought a gun or got it by LL, and then sent it to, say, South Africa, which after the war sold it to a U.S. importer, it would not carry any British proof marks. It might have a South African property mark (an arrow insude a "U") but sometimes such marks were hit-or-miss in wartime.
Jim