I didn't realize it had a known composer. So, I looked at Work's other two best known songs, "Marching through Georgia" and "Tramp, Tramp, Tramp".

The verse part of MtG is straightforwardly tonal (moving briefly to the dominant). The chorus (much more memorable) is hexatonic, but a different kind of hexatonic - the seventh is missing, so it's major/mixolydian.

TTT is hexatonic again, lydian/major, all the way through. The fourth only occurs as a dispensable passing note.

Work wrote tunes that caught on. He was instinctively using the techniques of traditional music to do it.

("Grandfather's Clock" is heptatonic, but like the other three it's in a plagal mode - Work seems to have had a thing about that).