Pretty sure they fall into the same category as the PTRS and PTRD rifles - non-restricted, but rare as hen's teeth. Also, ammo for them would be a case of custom milling your own.
Can't tell for sure, but that Enfield might very well be a No1 MK III. Although Canada was well on the way to transitioning to the No4 MK I by the time WWII started, we still had a lot of the older rifles in inventory, and especially at the beginning of the war there was a very big case of "if we have it and it shoots, use it" going on. I have a BSA built 1917 No1 MK III that was (as far as I can tell by the various stamps on the receiver and barrel), surplussed to Canada after WWI, had the barrel completely shot out in training between the wars, was re-barrelled by Longbranch at the beginning of WWII, got the C broad arrow stamped on it and accepted back into inventory.
Unfortunately, after WWII, Bubba got hold of it and chopped the crap out of the wood and literally ground off some of the stampings, so a lot of the history is forever lost on that rifle. I'm slowly bringing it back to military configuration as a long term project.
Most of the No1 MK III's went to homeguard type militia units and support battalions (transport and logistics), but not all. They floated around.