As to the song's subtitle (either "The Not Noel Coward Song" or "Not the Noel Coward Song" depending on which part of the Monty Python Sings CD documentation you read), I can offer the following: in the film The Meaning of Life, the character who sings this little masterpiece is listed in the credits as "Not Noel Coward".
This would suggest that "The Not Noel Coward" song is the correct subtitle, although the other version may have been included as a further sly joke.