I'm baffled Kohr - as I expect, are most others here............ I'm not quite sure that your rifle is rare or even scarce insofar as the different parts are concerned. In real terms, it's just another one of hundreds of thousands of these Mk1 rifles built in the UKduring the war. As I mention, you'll find those parts or combinatiuons of parts on thousands upon thousands of Mk1,1* and so on, up the scale of No4 rifles. As a matter of interest, I don't think that I'd call a 1945 No4 particularly early either! Nope, it's just another bog standard BSA made mix and match wartime produced No4 Mk1 rifle
What makes it interesting to collectors is the markings that indicate where it's been for a few years of its life.
Maybe the man who told you all this information regarding the mysterious rarity has been slightly mistaken. Maybe he could put his head above the parapet and explain his findings. They'd cause some interesting replies I feel........