This was one of the songs that my maternal grandfather would sing at our Christmas gatherings in rural Lancashire (late 1940's - 1950's). I have a rather poor quality recording of him singing it. The main difference with the text given above was his very lengthy (or so it seemed to me) chorus, which went:

With a hey tantivy,
Hard for'ard, hark for'ard, tantivy
With a hey tantivy
Hark for'ard, har for'ard, tantivy
Hard for'ard away, hark far'ard away
Hard for'ard away, hark far'ard away
Arise the burden of my soul
This day a stag must die
This day a stag must die
This day a stag must die

This would be sung after Christmas lunch when more than a few beers had been drunk by the adults and I seem to remember that the idea was to make as much noise as possible!