It was written by Harry Wincott, but I'm not sure if any of his lyrics survive -- love to see 'em if the have!

From a quick search it looks like Champion's lyrics and song recordings are the earliest, hard to say.
http://monologues.co.uk/musichall/Songs-W/When-Dun-Cow-Caught-Fire.htm

Wincott may have written the song for Champion to perform - http://www.harrywincott.co.uk/songs.htm