By 1828, the lyric had found a home in this collection:

The Universal Songster: or, Museum of Mirth: Forming The Most Complete, Extensive, and Valuable Collection of Ancient and Modern Songs in the English Language: With a Copious and Classified Index,
Which Will, Under its Various Heads, Refer the Reader to the Following Description of Songs, viz.

Ancient, Amatory, Bacchanalian, Comic [English], Dibdin's Miscellaneous, Duets, Trios, Glees, Choruses, Irish, Jews, Masonic, Military, Naval, Scotch, Sentimental, Sporting, Welsh, Et Cetera.
Volume II.
London: Jones & Co., 1829

where it is credited to "T. Moore."