Interestingly enough, the 1826 song (about a sailor) contains the line, "Wrap me up in my tarpawling jacket," tarpaulin jackets being associated with sailors.

Later versions of the more familiar song (or spin-off) often have "my old stable jacket," which is more appropriate to a lancer.

A check of several extensive data bases fails to reveal any connection to Whyte-Melville other than an attribution in the "Scottish Students' Song Book" more than a dozen years after his death. Though credited   to Charles Coote, the air is nearly identical to that of the anonymous "Rosin the Bow."

The British Library has sheet music of "Wrap Me up in my Tarpaulin Jacket" published by Hopwood & Crew, London, in 1884. I have no access to this. When Hopwood printed a "New Edition" with banjo accompaniment in or before 1892, the only names to appear were those of the arrangers, E. J. Symons (piano) and R. H. Davies (banjo).

The 1892 ed. has "Tarpaulin Jacket" in the title, but offers "old stable jacket" as an alternative in the lyrics, which concern a "lancer."