Try this link :-

http://lyricsplayground.com/alpha/songs/i/intheoldbazaarincairo.shtml

They credit it to Charlie Chester / K. Morris / Clinton Ford. I heard it recently on radio and looked it up on the web but as I recall, it was only one person singing it. The others might have been contributing writers (and with "cheeky" Charlie Chester, it seems very like the type of risque song he'd sing).