Thanks for posting that.
There was nothing very secret about the Class K: it was a beefed-up and speeded-up version of the Vickers-Berthier light machine gun, which was nearly chosen for the British Army (the Bren just beat it) and was used by the Indian Army. This was in turn based on the French Berthier LMG, which was developed before the First World War.
The Class K was a very good gun. It was test-flown with the big 300-round drum mentioned, and beat the .303 Browning for reliability. However, the wide drum would have caused problems to accommodate, since it would have interfered with wing structures.
When Class Ks were removed from aircraft, special forces in the North African Desert liked to attach them to their vehicles, as they liked the higher rate of fire and bigger magazine capacity compared with the Bren. Of course, they couldn't have fired very long bursts without running into overheating problems.