The tune (and the cadence of the lyrics ) certainly put me in mind of "Hey Ho, Nobody home":

Hey ho nobody home
Meat nor drink nor money have I none
Still I will be merry

the only music I can find for "Hey HO" the first line is the same as your canon, and the second line (of the copy I found) is NOT the version I have always sung. Yours is closer to what I sing....

I don't know the history of it, however...

MMario