When I did a search for "The Camels Are Coming" there were a few videos including this one with lyrics:

"The Camels Are Coming" with a distinctive C&W sound.

There also appears to be a religious song with the same name.

I think the big clue that it is not a simple mis-hearing of Camel for Campbell is that W E Johns wrote a book in the Biggles series with the title "The Camels Are Coming" and it was later made into a movie in 1934. As I recall from my dim distant memory the Biggles series was comedy and parody.