Several libraries have the sheet music described thus:

ELIZABETH (MY QUEEN)
English words by Irving Caesar**; music by Robert Katscher.
New York: Harms Inc., ©1931.

From revue: Wonder bar (adapted from the Austrian original).

[First line?*] She's the kind that boys romance with
[First line of chorus?*] My Queen Elizabeth has the neighbors out of breath

* or vice versa
** I suspect other English versions exist besides Caesar's.

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Allmusic.com, on the classical genre, lists the following song:

WENN DIE ELISABETH NICHT SO SCHÖNE BEINE HÄTT', song (a.k.a. "MY FRIEND ELIZABETH") by Robert Katsher
Which appears on 2 albums:

Arranged for brass quintet on "Karneval der Tiere und anderes" by Quintonic Brass (2003)

"The Golden Age of Light Music: The 1950s, Vol. 5 - Sunny Side Up" (recorded 1957; album released 2008)

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ELIZABETH
As performed by Debroy Somers* and His Band, on "My Friend Elizabeth" (2011)

My friend Elizabeth's
Out of temper, out of breath
Ever since she's found
Skirts must trail upon the ground.

She had a better set
Of legs than even Mistinguett.
Now she's got to hide
What was once her joy and pride.

This fad of over-dressing's
Depressing, distressing,
And catching men grows harder;
Their ardor's not so strong.

My friend Elizabeth's
Tired of life and prays for death.
How can she go wrong
Now that skirts are long?


* Debroy Somers was the band leader; I don't know whether he was also the vocalist. (In those days band leaders got top billing over vocalists.)

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I have also found references to the following recordings of ELIZABETH:
Bob Pearson and Alf Pearson, on "My Brother and I"
Fred Waring & His Pennsylvanians, 1931, on "Memory Lane"
Debroy Somers & His Band, on "Night Time Brings Sweet Dreams of You"
Humphrey Lyttelton, on "Just About as Good as It Gets!"
Emil Coleman and His Orchestra, 1931