I first heard the Marie Lloyd reference in a one woman show by Elizabeth Mansfield and she did consult with the British Music Hall Society Study Group. They would know more about the provenance of the story. As I can not find any reference the song itself in bibliographies on the music hall canon -it does not appear to be part of Marie Lloyds repertoire the story could be apocryphal possibly even made up by Marie Lloyd herself who had many run-ins with the entertainment and culture establishment.