I've had time to look at the relevant material now.
The 1951 song I was referring to earlier actually only uses the tune of Crawdad. It's called 'I wish I wuz' and it's by Sid Kuller and Lyn Murray. I've got 4 different versions of the sheet music all by different artists. The soccer/rugby chant must actually be based directly on Crawdad as its form is much closer to Crawdad than the pop song.