They were reasonable common in the Mid East in WW1 remained in reserve for decades. Some were issued for home defense in NZ early in WW2 due to lack of more modern arms.The Martini-Enfield made it into World War One, not the Martini-Henry. In fact, the Martini-Enfield was still in service with the Indian army until WW2 and Afghan tribesmen preferred to use them along with Lee Enfields to shoot at the Soviets in the 1980s; doubtless a few were fired at Coalition forces too.
Old Maxim guns in 45 caliber were fitted to Scouts to attack Zeppelins during the war,as at the time the .303 bullet didn't have enough incendiary payload to be effective.45 calibre Martini Henry incendiary rounds were made to attack Observation Balloons and were used before planes carried machine guns.
The Home Guard used some locally sourced Martini Enfields in their early days in the Midlands in WW2. Martini Enfields were used in early period training and by the WW1 equivalent of the WW2 Home Guard.
The Ottomans were not only using their Martinis in some second line units (some updated to use Turkish army Mauser ammunition) but some poor souls in Yemen were still using Sniders of which some were Turkish/Belgian converted Enfield rifle muskets from the USA civil war surplus sales including some sold to France in 1870, captured unused by the Prussians and sold to the Ottomans.