Written by Alan Melville? John Jowett? Music by Charles Zwar? Robert Gordon?
Lots of mystery surrounding this one.
Something by this title is available in a publication called Mixed Foursome: Items for Revue (Samuel French, 1951).
However, according to Alan Melville’s autobiography, Merely Melville (Hodder & Stoughton, 1970), this was the title of a song by John Jowett and Robert Gordon (although it seems to be more generally called "The Borgias are Having an Orgy".) It started out in a revue called Sweet and Low (1943), then was used in Sweeter and Lower (1944), was used again in It’s About Time (1951) and then in Sticks and Stones (1956).
Little wonder it shows
up so often—it is a hilarious song! Picture four members of the infamous
Borgia family sitting around awaiting the “party” they were about to throw
as you read these lyrics.
The credit for tracking down the info from Merely Melville, including the song lyrics, goes to Sonoma—thanks!