Hopekirk's songbook gives no background info. After other searches failed, I went to Levy. I got the sheet music by putting "put off" in the search box. "row with speed" or "put off put off and row with speed" works, but phrases with wi' doesn't. To get the info through Digitrad and Forum Search, keywords would be "Robert Allan" or "row wi' speed" (and of course "Queen Mary's Escape").
I don't know who Robert Allan was, but two songs by him were found.
ALISTER MCALPINE'S LAMENT (in the DT)
On the Banks of the Dee (1836) (in Levy)
~Masato