I have just heard from MCPS/PRS that their database cannot link author/composer details to a particular lyric/melody, so they cannot help further. Curses!
I think Landlady's Daughter is probably right about index confusion giving rise to the alleged two songs and we're probably still talking about only one, but I'm not sure how to take this further. The British Library Copyright collection, perhaps? Anybody know anything about this aspect?
In the meantime I'm going to pour myself a stiff drink and write another devastatingly witty book. I can only suggest that you all go out and buy one to distract you from looking for weird songs!