AKA "Dirty Old Torbay Men." Origin may be Irish. See www.thesession.org.
The Session

Many recordings.
Originally the Gmajor polka "Maggie in the Woods." AKA An BhFaca Tú Mo Shéamaisin?
Recorded by the Chieftains and Foggy Dew.

Lyrics from the Chieftains:

If I had Maggie in the Woods
I'd do her all the good I could
If I had Maggie in the woods
I'd keep her there till morning.

The Chieftains wrote an answering verse because they had a female in their group:

You won't have me, not in the woods
For I fear that you mean me no good
So go on back to yer dear old mum
And I'll see you in the morning.

Data from pages of The Session, linked top of this post.