Import mark from when it came into the states from England, must have seen UK service.
Fazakerley small arms factory logo
Savage arms logo
Inspector mark from BSA Shirley
Fazakerley logo and the number relates to the hight of the sight post.
Magazine - M/56 is the maker code for ww2 British contractor Cheney & Son. The serial looks like a Longbranch serial number and Longbranch did number their magazines but there is no other long branch markings. Might have been added by the importer.
I haven't seen the markings on the barrel before. Doesn't mean they're not original but they might have been put there by the importer.
After some research the barrel are import marks, also thought I'd add that all the serial numbers match on the bolt receiver/barrel, and mag. Also in agreement with all that you said, took me a some time and someone to point out that the "B" markings are actually a B overlaid in an L (Longbranch)
Thanks for helping me confirm the markings, always interesting trying to decider the history on a rifle based on its markings.