Les
There is a theory that Morris sides occasionally found themselves without a musician, and had to dance to songs.

But many Morris dance tunes are 18th or 19th pop songs anyway, and there are words to most of the Adderbury dances.

I unearthed one of them myself. Beaux of London City comes from a song with the unlikely name of The Knowing Maccaroni Outwitted, c1800
which starts, if I remember right:

You beaux of London City, likewise St James's Park
Give ear unto my ditty, tis of a frolicsome lark

On the original topic, I too remember playing Dingle Regatta in the 70's and 80's, and we never did any Hey Ho's. But as we usually played standing up, we didn't often do the sitting and standing bit either.