Some brief examination of J.H. Steward lead to the solution.
Established in London in 1852, Steward's were opticians and scientific instrument makers. The family business had a long history, surviving into the 1970s, but given that J.H. Steward became J.H. Steward Limited in 1913 it was assumed that the gauge pre-dated 1913.
From the early days of the Volunteer Movement and the subsequent formation of the National Rifle Association (1859), Steward saw opportunity to market his instruments, and telescopes were of particular relevance to the rifleman. By way of example, the following letter appeared in the Morning Post on 4 March 1863:
THE WIMBLEDON RIFLE CONTEST
TO THE EDITOR OF THE MORNING POST
Sir, – In your report of the result of the trial of small-bores at Woolwich in your impression of Friday last you state that the council of the Rifle Association have accepted my offer to give three of my "Lord Bury telescopes" as prizes to be shot for at the next Wimbledon meeting which is not quite correct. What I have done is, given them three telescopes of the value of 25 guineas, and offered to lend them 40 of my best telescopes for the use of the competitors at the next Wimbledon contest, which offer they have done me the honour to accept. By the insertion of this you will much oblige your obedient servant, J. H. STEWARD. 406, Strand, March 3.
Given that Steward's had a long standing relationship with the National Rifle Association (NRA) the gauge was thought to be associated with rifle shooting. It is marked "Prov. Patent", but without date or number. However, based on the background above and research of patent information under Class 119, Small-Arms, the puzzle has been solved.