Ol Tom: I have seen those rifles before. I believe that some English firearms firms, Churchill being one of them, took representative samples of both the MkIII #1 and the #4 Mk Is and sporterized them. Those I have seen seemed to have heavy barrels not of the military contour and it looks like they were either re-barrelled or the military barrels were cut and crowned English style (flat). They could have been the original barrels but I couldn't tell.
I was interested in one at a local gun shop before the last hunting season but let it go to a young man who had no idea what he bought. A week later I was at the range with my own 303 and along comes you know who with you know what. He needed help with his new 'no-gunsmithing scope mount' and sighting it in.
Well, that rifle shot almost as well as my 1966 sporterized #4 MkI did. He was using Winchester factory ammo, which I don't hold in high regard, so his groups were not as tight as my handloads. My handloads in his rifle put 3 right on top of each other, just a my rifle does. The kid was sold on the caliber and is now into reloading. Don't know how he did this year but that was a fine looking and fast handling package.
I don't know if these were excess weapons that were not issued. If they are, they are most likely fine examples of the SMLE, since they may not have seen battlefield use.
How fond are you of this rifle????? Just curious. Hope this helps. Mikey.