Bert's tune sounds like he tried to sing the one collected by Ella Bull in Cottenham , Cambridgeshire in about 1904 from Charlotte Dann and failed to reproduce it accurately.( A not uncommon occurrence with Bert.)
The Cottenham song ( the only version collected in England to my knowledge, apart from a fragment in Hampshire) is a straightforward major mode song with the last two lines being repeated - this was not done in either Bert or Martin's version.
Bert went to the Child ballads to pad out the text which comprised only the living will verses and fragments of the earlier part of the song. Charlotte called the song "Lucy".She said she did not remember where she learnt the song - not surprising considering its content and the fact that she may have been aware of similar activities in neighbouring fenland families.
Charlotte had been approached by the nice young middle-class Ella Bull, the daughter of the family where she was once a servant in the mid-1870s who remembered her singing the songs as she worked in the house. I can imagine it was a great shock for Charlotte to be asked to repeat the songs for prospective publication when she was visited by Ella in the early years of the 1900s.