a quick reserach indicates.....
Looking at all of this dispassionately, a few things on both of these guns say they were not UK military trial guns in any way:
1) The commercial proof on a 1945 dated barrel,
2) The use of Ross buttstocks. Not UK standard in any way.
3) The lack of any kind of front bearing allowance, No 1 MK III barrels were well understood to not shoot well without damping of the barrel between in middle internal band and the front nose cap. Given that there would be no way a metal stock would be designed that did not provide for some sort of barrel damping forward of the middle band, at least on a full length barrel.
4) A check of Reynolds book “the Lee Enfield rifle” shows all the metal stock trails were with the No 4 and occurred in 1943. These attempts were abandoned after 1943 due to various difficulties.
So that leaves the possibility that this is in somehow a Canadian effort. There are several good reasons why this would not be the case:
1) Canada had no shortage of lumber, none whatsoever.
2) In the June and October of 1943 holding reports the total stock of CA No 1 MK III rifles was 15,798. They had fewer No 1 MK III rifles then Ross rifles of, which ~41,000 were on hand. By 1943 the No 1 MK III was a surplus item, and far fewer were in stock then M1917 rifles and even Ross rifles. In 1949 the holding were listed as 11,000, of which only 2,280 were serviceable.
3) By the end of the war ~900,000 No 4 MK I* rifles had been made of which 330,000 were sent to the UK, there was a vast surplus of No 4 rifles in Canada. There simply was not any requirement for No 1 MK III trial rifles of any kind.
4) The DCRA made the No1 MK II obsolete for competitive shooting in late 1946, thereafter all shooting was done with the No 4 MK I*. So it is unlikely done for DCRA.
So what evidence are there these might have been some sort of post-war commercial/home build?:
1) The use of a commercially proofed 1945 barrel.
2) The use of Ross butts. In 1946 the Canadian Ross rifles were transferred to the War Assets Corporation, which was supposed to dispose of them. According to “defending the Dominions” most of these rifles were broken up and sold as scrape. It is quite possible in 1946 that there was a number of broken Ross buttstocks available for next to nothing (scrap value). Having a supply of unusable broken Ross buttstocks seems to be the only possible reason for making them fit the No 1 MK III.
3) The inclusion of various barrel bearing in the casting between the barrel reinforce and the internal barrel band might have been and attempt to dampen the barrel vibrations. The Martian nodal bedded target rifles that were fairly well known in Canadian target shooting circles between the wars. If the chap doing this work thought he might be able to dampen the barrel by inclusion of nodal bearing points behind the internal barrel band, he was following a concept well known at the time in Canada.
4) Lastly thought he casting may be well carried out, the lack of a firm fitting between the buttstock socket and the front draws seems to indicate a lack of the most basic bedding concern according the EMERs. It is hard to see any military trial piece not attending to this detail. You can literally see light through the gap between the action body buttstock socket and the rear of the aluminum stock piece on both examples.
On the other hand I have known folks that claim relieving this fit on the No 1 and No 4 will make it shoot better at the close ranges, in the 100 to 200 yard region where hunting rifles are commonly used, as long as the fit of the forend to the barrel is fairly tight. That is purely a hunting rifle type build.
So overall considering what little facts are available, these examples have to me, all indications that they are local Canadian commercial or garage shop efforts.