The song was written in 1927 by Herbert Farjeon and the girl that inspired the song was Edna Deane, a ballroom dancing champion.
:I've danced with a man, who's danced with a girl, who's danced with the Prince of Wales.
:It was simply grand, he said "Topping band" and she said "Delightful, Sir"
:Glory, Glory, Alleluia! I'm the luckiest of females
:For I've danced with a man, who's danced with a girl, who's danced with the Prince of Wales.
:My word I've had a party, my word I've had a spree
:Believe me or believe me not, it's all the same to me!
:I'm wild with exultation, I'm dizzy with success
:For I've danced with a man, I've danced with a man-
:Who
:Well, you'll never guess
:I've danced with a man, who's danced with a girl, who's danced with the Prince of Wales.
:I'm crazy with excitement, completely off the rails
:And when he said to me what she said to him -the Prince remarked to her
:It was simply grand, he said "Topping band" and she said "Delightful, Sir"
:Glory, Glory, Alleluia! I'm the luckiest of females;
:For I've danced with a man, who's danced with a girl, who's danced with the Prince of Wales.
You can find the song over the credits of Edward & Mrs Simpson here:
http://www.youtube.com/watch?v=hjogyfx-mFkI found no info on imdb.com on who sang the song for the production or whether they grabbed an old recording.