It was "Minstrel Boy," which is annoying. At the end of the story, after the MWWBK is killed Kipling had his friend Pinky Carnavon sing, "The son of man goes forth to war," which is clearly to the toon the old missionary hymn in which it is the "son of God. This fits the theme of the story, which is hybris. But the people who made the movie apparently thought that the use of a hymn tune would offend someone, so they had him sing to the tune of the "Minstrel Boy." That has nothing whatsoever to do with the theme or subject of the film.

Especially since it is a sentimental tune about an Irish Catholic, and the story was about a Welsh Freemanson!

--- Link fixed. ---