Roud lists one of the copies by Harkness, the other two with no information. Martha Vicinus repeats the 1804 date and Roy Palmer the 1804 Swindells attribution (though the version he gives (Sounds of History) says no imprint but released by Harkness). The three at the Bodleian (one of which is Vicinus' source) have no imprint.

I don't know if there's any more information on release of the ballad. Perhaps Steve Gardham can help out?

Mick