I have finished the book but am otherwise not very well read on the subject.

Can someone direct me to examples of songs for which there is good evidence of them starting out as 'popular music' (theatre, pleasure garden, music hall, etc) and then having then been collected from an oral source in an 'improved' form?

I am not doubting they exist, but they are harder to recognise than those that seem to have become garbled so that they no longer make sense to a listener.