I came across a reference to "Green Ribbon". It was in the context of Irish Political songs but given the scenario it would have to be a derived version of a well known song.
I too first heard the cockney version, Charles Chiltern is credited with the costermonger version in his book of songs penned originally for a BBC radio series in the 50's. Peter Dawson (opera singer c 30's) sang it but I asssume he was singing an earlier version than the Chiltern arrangement. The chorus is just similar enough to ensure you can't get away with it when the audience only know the Steeleye Span version.