Here's my transcription of what Jon Boden sings on A Folk Song a Day. I have to believe this is the Mercer song, and that Mercer's song does not come form older roots. I'm going to need help on this because there are parts I don't understand - please post your corrections below and I'll add them here.

QUEENIE (STRIP POLKA)
(Johnny Mercer)

There's a low-down [tavern???] where the boys all go
To see Queenie, the star of the burlesque show
And the highlight of the evening is when on the stage she trips
And the band plays the polka while she strips.

    CHORUS
    "Take 'em off! Take 'em off!"
    Cry the boys at the back;
    "Take 'em off! Take 'em off!
    Be your natural self."
    But Queenie is a lady, and it's only pantomime,
    So she stops!
But only just in time.

There's another side of Queenie that the boys don't see,
She dreams of a cottage, surrounded by trees;
But the payment of the mortgage takes an awful lot of chips,
So the band plays the polka while she strips!

    CHORUS
    "Take 'em off! Take 'em off!"
    Cry the boys at the back;
    "Take 'em off! Take 'em off!
    Be your natural self."
    But Queenie is a lady, and it's only pantomime,
    So she stops!
But only just in time.

    Some day, Queenie will fall;
    Queenie, pride of them all.
    Some day, church bells will chime
    But only just in time.

Words and music by Johnny Mercer, 1942 - adapted by Jon Boden.