The British Library has a copy of the sheet music, undated, giving the following attribution:



    Title: The moon shines bright on Charlie Chaplin. : [Song.] / Words by Edward Stanning and Thurland Chattaway. To the melody of Kerry Mills' 'Red Wing'.
    Author: Kerry Mills, 1869-1948.
    Subjects: Dewey: 780
    Publication Details: London : B. Feldman & Co., c.
    Language: English
    Uniform Title: Red Wing; arranged

Mick