I had until recently one in the X32--- serial range - there are quite a few in that range too - must have been a run of better than usual rifles from BSA Shirley - peacetime as someone mentioned. Everything on the metal was as per yours, even the placement of the 'X" where the SN is stamped on the bracket. Scope number was 23--- also.
The bolt you have there is post-war Belgian made. If you look on the underside you will find a small square stamp IIRC, but the sharp edges around the hole are the tell-tale feature.
Your forend has been replaced at some point, if it is not clearly numbered to the rifle. Butt markings are a bit hard to see, but you have what looks like a five digit number starting with "2" and below that what looks like "13041". If the upper number matches the scope and the serial number of the rifle is on the butt 'tongue' where it goes into the socket (take the butt off and have a look), then you probably have the original butt ; if you have the S51 stamped on the underside as mentioned above. Why the 13041 would be there I don't know, if this is the original butt. Surprising that those numbers are not more clear considering the decent overall condition of the rifle & scope.
The small V shaped piece of wood screws onto the left side of the removable piece of wood that supports the rifle in the chest, with the V facing downward. This piece is to hold the case for the Telescope, Scout, Regiment/Signaller's/G.S. (depending on what was supplied; they're all about the same.) The other end of the telescope case tucks under the piece that is attached to the left end of the chest. I can send you some photos if needed.
The other three pieces screw onto the inside of the chest at the butt end and keep the butt aligned, so to speak. Whoever started to refinish the chest, probably didn't put them back on because being screwed on before the chest was assembled originally, they are a b---d to get on and off when the box is assembled. Use a 1/4" ratchet with a suitable flat blade driver socket.
The large label of course goes on the inside of the lid, centered. Make some high-res scans while you have it off the lid. If that is the original hand-drawn label for the scope adjustments next to it, I'd suggest doing the same for that. Not often seen in a scannable condition off the case/chest.
As for scopes, get Peter Laidler's books and if you are good with detailed work, you can probably do some of it yourself. The index plungers stick sometimes from dried grease, but this is not hard to fix, and is the usual reason the knobs/drums stick. Removing or cleaning the reticule is tricky, as the crosswires are extremely thin and easy to break. If yours is clean, leave it be. Lenses could probably do with a cleaning after 60 odd years, but taking a "W" scope apart ain't easy as everything is sealed with 60 year old mastic, which can take little gentle heat to soften etc. Once apart, the seals are broken, so the "W" is now "SW" for 'sorta waterproof'.
If you or someone you trust travels to the UK, you could take it over for repair. Peter Laidler posts on the jouster.com forum and you could contact him there. Fulton's is his drop point for scopes etc. I hear, but they will make you pay for the privilege. He says he's sick and tired of doing them, but he is very generous with his time and resources and no one else has stepped forward who has his experience and expertise. Anything shipped to the UK for repair and re-export has to be very clearly marked as such, otherwise HM Customs charges whopping import duties etc.
Too bad about the chest refinish, but people do these things. I had one someone had gone over with an angle grinder. Sometimes there are markings on the chest that will show what country it was supplied to and when and even what route it took to get there. One of mine has the very same Canadian Pacific Steamships Special Stowage sticker, with number "7" in the same blue pencil, so it may have been in the same shipment as yours. It was not the rifle I mentioned above, but one that had never been fitted with a scope, though it came with a mismatching Mk3 scope in the same Case, No8 MkII.
I doubt these are ex-Canadian rifles. Probably a bunch of all sorts imported from the UK in the late 50s or early 60s. I doubt the UK govt. sold off complete matching sets at that point, but who knows.