Your point-to-point Broad Arrows are the Army's "Sale Mark". They are proof that the rifle, once Government property, has been legally sold out of military Service and is not a stolen rifle.
Alex Martin of Glasgow was indeed a gunsmith for the gentry. The shop made really excellent target sights and did sniper conversions for both World Wars, mostly the First, if I recall correctly. They also were agents for the Ross Rifle Company; a friend in Lahore owns an Alex-Martin-marked 1905 Ross sporter in .35 Winchester.
The fellow I shoot with is a grand-nephew of Alex Martin, visited the shop in 1947 or '48, told me of the long line of chaufeurred Daimlers, Rolls-Royces and Bentleys waiting outside the shop while the Great Ones had their needs catered to and the servants hauled in the bags of money. My friend was from a side of the family generally not mentioned, but he was allowed to visit the shop and was shown through the workrooms as well as the showroom and he has never forgotten it.
Further, Alex Martin was the inventor and patentee of the Martin Ribless shotgun, said to be a notable advance in sporting guns. They are very rare and hideously expensive.
I have a Lee-Metford Mark II myself, a commercial from BSA and it hae nae guid Scots thistles mark'd 'pon it. I rather think this could have been added in Glasgie.
I haven't seen your gun but perhaps you might have it looked at by somebody who really knows these old-timers. Martin's might have cut the barrel. Never know.
Have fun!