The question isn't whether Hotchkiss MGs were used in WW1. The issue is whether they were used on British aircraft.
The answer is "in a limited way." While the Hotchkiss was the standard MG of the French air force, the principal airplane flown by the British (and Americans) armed with the Hotchkiss was the French deployed in 1916. Many of the British planes, however, were equipped with the more familiar Lewis gun. The Royal Naval Air Service operated a number of French Breguets and Caudrons, also armed with the Hotchkiss
One prominent unit to employ the Hotchkiss-armed Nieuport was the American Lafayette Flying Corps of the French air force. When the U.S. entered the war, this unit was transferred into American service.
The collectors of the only two *first-hand* examples of the song I've seen that mention the "Hotchkiss" had both been associated with the Lafayette F.C.