I think I can shed some light on why only the chorus survives orally.

Like "Chase Me Charlie", this is a "song" taught to me by my mum.

Things often survive because they're useful and, like "Chase Me Charlie" (for which I have a verse and chorus), it was sung while dancing to the tune. Redwing was incredibly popular in East Anglia for dances and that's where she sang the Charlie Chaplin chorus.

By the way, she was taught "country dancing" by a teacher from the village who was scarcely older than her. The same teacher, somewhat older, also taught me the same dances. However, her "Ballroom" dances (which is mainly what was danced in village dances in the 40s) were taught to her by a peripatetic "dancing master" who travelled round the villages teaching youngsters to dance.

:-)
Ian