During WW1 the British Royal Navy issued them for the use of the on-board Royal Marine contingent to use for mine disposal, boarding and shore-party activities. The RN Division of the days was large part of the Fleet and took part in the Gallipoli campaign with great loss of life. They are, safe to say, exceedingly rare and valuable guns to identify.
In addition - this might be useful - from TonyE -
As Joseph said, the Royal Navy had a mixture of Lee-Enfields (the long rifle) and SMLEs at the outbreak of war. Winston Churchill was First Sea Lord and on 25th November 1914 he wrote a memo in typically direct language as follows:
THE RIFLE SHORTAGE
The following course is to be adopted:-
1. As soon as the War Office are ready to hand over the 50,000 Japanese rifles, the whole of the rifles, long and short, whether used by sailors or marines, on board H.M. ships at home and abroad, will be collected and brought on shore to the Royal Naval Ordnance Depots. The Japanese rifles will be issued to all ships in their place; there will be no rifles of any sort on board H.M. ships other than Japanese.
2. From the British rifles surrendered by the Fleet, 15,000 short .303 charger loading rifles will be set aside for the Royal Naval Division, i.e. one rifle for each of 12,000 men, plus 25 per cent for reserve and training. All the rifles now possessed by the Royal Naval Division will then be surrendered to the Ordnance depots for the 15,000 short British .303, and no more.
3. There will then be handed over to the Army 57,800 rifles, of which 9,000 will be short charger loading.
4. The 50,000 Japanese rifles will then be issued to the Fleet in the following proportion:-
One rifle for each marine and one rifle for every five sailors, ships on foreign service receiving one rifle for every three sailors. The rest of the rifles will be issued as required to trawlers and auxiliaries, and kept in the Royal Marine and Royal Naval Ordnance depots.
The Fleet will thus be completely re-armed with the 50,000 Japanese rifles, and the Royal Naval Division with .303 short rifles ready for field service.
Let me now have calculations worked out on this basis; and draft a letter accordingly to the War Office.
November 25, 1914 W.S.C.
The navy did not like the Arisaka very much and when Britain started shipping all the Japanese rifles to Russia in late 1915 the navy had theirs replaced by Ross Mark IIIB rifles.
These were used by the RMs on board all capital ships and also for destruction of mines as previously mentioned. there were however other small arms used by the navy. They had 21,000 Winchester Model 1892 rifles in .44-40 calibre and about 5,000 Model 1894 rifles in .30-30 calibre. These were mainly used for arming boarding parties as they were short and handy and would not have needed any great range.