Wow--great rifle!
Well, obviously a Boer War veteran, but doubtful that it's a Jameson Raid rifle. First, the BSA records indicate that they sold Lee-Speed sporting rifles and military configuraton Lee-Metfords to the BritishSo. Africa Company prior to the raid, but no evidence of trade pattern carbines in this order. Anything is possible in the world of Lee-Enfields, of course, but unlikely. But the more compelling evidence is that this rifle is marked BSA Co. on the wrist, and at the time of the raid, the company was known as BSA&M, and the rife would have been so stamped. Much more likely that this carbine was privately purchased (by someone on either side) on the eve of the Boer War, and it could have changed owners along the way. I am also curious to learn more about "J Kelly, Trooper 2029 0f the Doyle Scouts." The number on the buttstock clearly indicates service life (as if the carving were not sufficient evidence). Private purchases were not necessarily to an individual---could have been to equip a unit.
FWIW, I have collected info on other Lee-Speeds with 13xx serial numbers and they are all trade pattern carbines too. Now the encircled V mark is not a proof mark (the Proof House didn't use such a mark). I wish I knew exactly what it meant, but I have been researching it for some years without success. Each time I think I have it figured out, I'll discover some new rifle specimen that sinks the hypothesis, and it's back to the drawing board. I think--for now--it's best to concur with Ian that it is a private BSA viewer's mark. But there is still a mystery to solve, because not every BSA barrel has it. [For everyone asking why the Lee-Speed book is so much delayed, it's because I'm trying to crack this puzzle!] By any chance is there an encircled E mark on the other side of the barrel? Could you post a pic of that side?
Four more questions: 1) Is there a number or letter on the top-rear flat part of the action (where the bolt slides in)? You just need to raise the bolt handle and look beneath.
2) Have you removed the fore-end? If so, I'd like to know if there are any numbers beneath the wood, where the barrel meets the action.
3) Is the bolt matching? If not, what is the number on the bolt handle?
4) What is the barrel length, and what is the overall length? Let's make certain it is actually a trade pattern carbine.