The first weapons to leave the Britishsmall arms factories as original with phosphate and baked Suncorite paint applied were Mk.5 Sten guns. Guessing mid to late 1944. Full blown FTR programs after 1944 would have included the baked paint finish over fresh phosphate, (Parkerizing), as standard rustproofing. I've seen many wartime date No.4 rifles that were not refinished with phosphate prior to getting a baked paint job. Guessing the original blue was good enough to just degrease, prep, paint and bake them.
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I just refinished a 1942 British owned Guide Lamp Division of General Motors M3 SMG in fresh phosphate and Suncorite 259 paint. It looks lovely and is on the way back to the client "as we speak". I refinished two magazines too which HAD to be range tested! First time I've ever fired a grease gun. It's a flawless runner and quite accurate once you get the hang of it. It has a much slower rate of fire than a Sten or L2A3. I told him it needs a period correct suppressor like the Z Force guns used by the Australian, New Zealand and British forces in the Pacific Theater of Operations during WWII.