The rifle started life as a BSA Shirley or Faz Mk1. If the OP takes the barrelled action out of the woodwork & has a look at the draws we can tell tell which of the two. If they are asymmetrical in shape then it's a Faz; it they are symmetrical it's a BSA Shirley. There's an outside chance of an early Savage or perhaps a POF(though I must admit I don't know if POF made Mk1 rifles or Mk2's or both). Much more likely BSA or Faz. The FTR marks are IMHO also likely to be BSA. How & when it got to Canada
I've no idea.......