There is nothing presented so far to indicate this is A British Military rifle. Rather more by what hasn't been presented supports Boer issue,
The markings on the rifle action should clearly Identify the rifle for what is. If it is ex-British military it will be clearly marked right and possibly left side what it is. The OP made no mention of these type marking which would have been conspicuous and prominent and I would have thought reported by the OP. Absent those marking I will say this is not a British Military Martini.
Absent these British marking it is also not a Mk anything. It my be similar to a MK pattern but only the British military rifle is a MK.
The commercial rifles could have parts of several different patterns all on one rifle and be correct and complete.
That WR number is not British Military. All British Military Martini's will have the serial number marked on the front of the action under the fore stock wood. The number or part of the number will appear on the barrel usually on the bottom and on the bottom of the rear sight ladder. The number will be up to a three digit then a letter and three digits. Three digits from 001 to 999, then A001 for 1001. Z999 would be 26999. There are some double letters. AA001 would be 27001.
OVS and and ZAR serial number were prefixed just that way, with OVS and ZAR and were quite large. . I have seen reference to WR prefixed markings before. My Memory says the WR is for Westley Richards. I cannot find a reference to that right now. I also seem to think I may have seen the these WR serial numbers issued by SAPS for rifles with no serial number for registration purposes.. I'll look around a bit and see what I can find.
Westley Richard as well as others provided the Boer Republic with large numbers of arms of all types and especially Martini's. These were in a large part unkmarked or other manufactured arms. Westley Richard also provide the Especially Made for ZAR rifle made with the Francotte detachable action. The rifle pictured is clearly not one of these. Here is what the action of one of those look like.
Sling location on a Boer rifle would be highly variable and irrelevant and does not indicate British military service.
All the answers to what this rifle really is are on the rifle. Clear pictures of the markings and their location will identify this rifle.
The fact that British military Markings were not reported on the receiver also heavily discount that it is a Khyber Pass rifle. The fact that it came from SA points away for KP origin. KP Martini's are almost unheard of in SA. I have been trying for a year to get one sent down to a collector in SA as he has never seen one.
My Westley Richards Mk II pattern Martini rifle has a similar looking front sight but is a 577/450.
Given the information presented so far the only definite thing that can be said about this rifle is that it is a Martini. Everything else is pure speculation.