It is a 1910-16 Enfield made Sht.LE Mk.III. 1910 is earliest because it has a George Rex proof mark (King George V 1910-1937) on the left receiver ring. It is a Mk.III which went to III* in 1915/16. There is a marking under the III that has some relevance but I cant read it. '18 ?? '12 ??
Looking at the left butt socket '37 denotes that is went back to the factory for significant work in 1937. There should be a tiny inspector stamp close by to the '37 which will tell as to which factory.
It has had a barrel changed and fitted in 1942. Enfield made barrel. It was renumbered to match the receiver. There are a number of RSAF inspector markings on the right hand barrel reinforce which often indicates that there was some work done on the barrel, chamber or sights.
The rear sight bed is a post 1925 Enfield unit that was pulled out of a parts bin and fitted. While the base had been sitting in stores, it was picked at random as part of a 10% of inventory inspection and thus marked o/l\o. The sight leaf is a replacement too, a good used part out of the parts bin, old number cancelled then and renumbered to match the rifle.
BSA on the underside of the barrel is likely an ownership marking for the British South Africa Co.. An outfit organised much in the same way as that of the East India Company. Is there a three digit number adjacent to it?
Single hand stamps, so we cant rule out that it could be simply a previous owner's initials (Bertram Samuel Atkins?).
This rifle was probably purchased and reassigned duties post WWII. There are no commercial proofs apparent, so this has been sold out of service through channels outside of the British gun trade.