Yes, indeed. Auchendoon, Harlaw, &c were the exceptions I mentioned.

These came to mind without much prompting. I am sure there were more I have forgotten for the moment ~~~

Many cumulative songs like Cosher Bailey [Did you ever see?] or QM's stores have disobliging variants to verses

BGW
Queen of all the fairies [aka Leave it alone, play with your own][tune Blaze away]
Mary in the mountain glen [They called the bastard Stephen]
3 old ladies locked in the lavatory
Chastity belt
Sexual life of the camel [tune Eton Btg Song]
Eskimo Nell [to tune Annie Laurie]
Good Ship Venus
My god how the money rolls in [tune Bonny over ocean]
Little Angeline
Roll me over
Caviare
Sweet violets
One-eyed Riley
Christopher Robin variants
In the south of France [aks When your balls hang low]
Hitler has only got one ball [tune Col Bogey]
Where was the engine-driver?[ ditto]
Boolox & the asame to you [ditto]
Inky-pinky parleyvoo [aka Mlle from Armentieres]

~M~