As a frequent visitor to the Sheridan or Davenport household many years ago, I often heard Percy singing this song & I have no doubt Lynn & Bob learned it from him & it went from there- no idea about the source of the song though....
I do remember about 1968 standing next to Percy at the King's Head club bar in Islington when a small lump of plaster fell from the ceiling, narrowly missing our beer!
that pub went for years after 1971 ignoring decimal currency- all prices were in pounds, shillings & pence- I wonder if it still is?

The current 'theatre pub' was a pretty dilapidated boozer then & in the course of our conversation Percy said 'I've been to London before, you know'. It surprised me a little- older people didn't travel much then but then he explained 'on me way to the war'.