Have one of these, too, in 30.06, with BSA trademark. Wish I could find out more history, as in where the action was originally made, when BSA marketed them, and if they re-barreled and re-stocked them, or did they merely re-work surplus rifles. Even sent an email to BSA couple years back, but no answer.
Anyway, they are terrifically accurate, and the actions are incredibly strong.
I had mine customized. He had a hellluva time re-bluing the action because, he said, the steel is so hard. Told me these are very good actions that can handle pretty much any caliber that will fit them.
Mine had a nasty habit of failing to pick up the next round unless I worked the bolt with some authority, which would snap the shell into place. I'm told this is because the magazine originally was designed for .303 ammo, which is rimmed, and thus a bit wider. Consequently the 30.06 staggers a tad too much and can slightly bind, causing them to stick a bit. At the time there was no solution in the aftermarket for this. I carved out a shim for the side of the magazine from a bleach bottle, smooth slippery side toward the cartridges, which did improve it. Only did one side, should have done the other, too. Couple spots of glue, always stayed in place.
There also are good replacement triggers for these. I went with a Dayton Traister, although for some reason it required modification to fit the BSA. This was a mystery to the guys at Dayton, but they were great about it, made the mod I specified, and sent back to me. Worked good. This was over 20 years ago, and perhaps they've since learned more about these particular rifles. There are other options for these, too. Well worth it, as the original two stage trigger is, IMHO, fairly awful.
I'm pretty sure there's aftermarket stocks available, too.
And lastly, I understand that these can be modified from #### on close to #### on opening like just about all other rifles, which probably is a good idea. Also, some smiths, when customizing, will straighten out the dogleg bolt handle, and trim the magazine to straighten out the lines of the stock to a more conventional style...which will decrease the 6 round capacity of the mag by one, no big loss there.
One last tip: My scope ended up with a bent tube. Bushnell told me to have the mounting surfaces checked for proper alignment. Turned out that they were right; when I had it customized the smith found the surface at the rear of the action had been poorly machined and was causing torquing on the scope. Had I paid proper attention installing the scope, I'd have discovered this. He trued it up for me. Perhaps something to watch for on a BSA sporterized action. (One of the reasons I now always use Burris Signature rings, which automatically compensate for misalignment and prevent such damage. No lapping and messing around required.)
These are very good rifles, with terrific potential. I wouldn't hesitate to look into reworking it, and ending up with a one off rifle that's all your own.
Ultimately, I got too fancy with mine, which made me sensitive to some of the beating a hunting rifle inevitably takes. I came across a deal too good to pass up on a Vanguard 300 WM, and thus this puppy has spent most of the last couple decades as a show piece in my gun safe.
I'd bet that Ellwood Epps would be a good place to start. I understand he's an expert on the Lee Enfields, and may know a lot about these particular rifles, too, given there are so many of them around in Canada.
http://www.ellwoodepps.com/
Again, don't underestimate the quality of what you have there.
Indeed, back in Lloydminster, before I fixed it up, I took it to a turkey shoot at the club one day. Entered two events against 9 other shooters, one at 100 yds, another at 200 yds. Pretty stiff competition, Sakos, Weatherbys, huge scopes...mine had a Bushnell Scopechief 3x9 at the time. A friend did up some handloads for me a couple days earlier just for the event. Just two boxes, picked a formula from his guide book, and we went with it. I won both rounds. At 100 yds, three of us scored 30, but my group was the tightest. And I scored the highest at 200 yds into a stiff crosswind. Needless to say, my relatively crude looking old rifle, by comparison, was getting some pretty disgruntled looks from the rest of the competitors. Heh! I love it when that happens!!! But I was very cool and sportsmanlike about it...