The "Airman's Song Book," Collected, Edited and with an Introduction and Explanatory Notes by C. H. Ward-Jackson, Music Edited by Leighton Lucas, Revised Ed., 1967, offers this explanation (already noted in part by Toadfrog):
"Many of these songs were not so much composed as evolved over a long period and often in various places. Most people would say (for example) that "Bless 'Em All" dates from the second World War and they probably would not particularly connect it with flying. Yet it has been the unofficial trooping song of the R. A. F. from the beginning in 1918. During the broadcast of the R. A. F.'s 25th birthday anniversary celebrations in 1943 Mr S. P. B. Mais (ex-R.F.C.) pointed out that it originated in the Royal Navy Air Service, written in 1916 by Fred Godfrey. That version was not for publication [Fuck 'Em All] and it was unknown to the public till the late 1930's when it appeared in a completely clean pinafore. Meanwhile, airmen had put all kinds of words to it, the essence of which is not unfairly reflected in the published version." Pages xiii and 136 (Bomber version, WW2).

Original(?) words to "Fuck 'Em All" in thread 10366, Guest Q: WW2 Songs
A version close to the original in thread 3282, Guest L: Veterans' Day

This book has all of the old airman's songs, including "Who Killed Cock Robin" and The Mountains of Morne," as well as "The Ragtime Flying Corps" from the 1916 period.