That is a rifle which was SOLD BY the Alex Martin shop in Glasgow. They bought them from BSA, worked them over completely to their own standards.
You could count on any BSA SMLE rifle to turn in 2 MOA. By the time Martins' were finished with one, it was a world-beater, in the same class as one tuned by A.G. Parker or W.W. Greener or Holland & Holland. They were all in the very TOP rank of shops building the finest in Service Rifle competition rifles.
Service Rifl competition was something we seem to have no longer, at least for the great old .303s. The rules stated that the Rifle should be the standard Service rifle of the period. In the case of the SMLE, it was factory-fitted with an open sight. An aperture Sight could be fitted; that was in the rules, but the entire rifle had to be returnable to combat "Issue" condition with no tool other than a screwdriver.
Ammunition for the matches was ISSUED to the shooter, 12 or 17 rounds at a time: 12 rounds for a 10-shot target, 17 for a 15-shot match, giving 2 sighters in each case. Sighting shots had to be called BEFORE they were fired. Everyone shot the same ammunition; possession of even a single round of different ammo disqualified the shooter from the entire match. The ammunition itself for the shoots was selected from ammunition already on hand. There was NO special Match ammunition made, unlike in American competitions. Matches were shot at ranges from 200 through to 1200 yards.
If your rifle did not "like" a certain Lot Number of .303 ammunition, you were SOL. This is why the rifls were "adjusted": so they would handle ANY Service Ball ammunition they were fed..... and do it to a MAXIMUM dispersion of 2 MOA, although MANY rifles would do 1 MOA. Yes: with iron sights.
The shooters had to be prepared to put up with anything that might be in the offing: good light, bad light, failing light, following or heading wind...... or a switching cross-wind...... mirage, mirage and wind combined.
It was the most brutally difficult competition in the world..... and the rifle was built to WIN under those circumstances.
Firing pin? Nothing. Standard SMLE firing pin will fit and work fine: $20 installed.
A set of Alex Martin receiver aperture sights, though...... well, that is another matter. They do exist, but they are few and far between..... and they are WORTH whatever you pay for them.
SOMEBODY had REALLY good taste in Rifles!