It is as I said above (though the posts are out of sequence now): early part of the 19th century. It was used in Alan Cullen's play The Stirrings in Sheffield on Saturday Night as also mentioned; there it was set to a new tune by Roderick Horn.

As to whether it's strictly speaking "traditional" (outside the Grinders' Misfortune Society, that is; and however long that lasted), I don't know; the words I quoted were taken from John Wilson's edition of The Songs of Joseph Mather (1862) and published without music (and minus the first verse above) in Paul Smith, David Spalding and Frank Sutton's Cum All Yo Cutlin Heroes: Songs from Sheffield and District (Sheffield City Museum, 1967). Apparently David Spalding also set a tune to it, but I don't know what that was. The use of Tramps and Hawkers was Paul Davenport's idea, I think.

There's no indication that Mather (who died in 1804) wrote the words, which were included in a separate section of "miscellaneous songs relating to Sheffield". The song seems to have been long forgotten until its revival in the 1960s.