The song appeared in Joseph Ritson's Bishopric Garland, or Durham Minstrell (1789, and various subsequent reprints), as 'A New Song, called Hark to Winchester, or, The Yorkshire Volunteer's Farewell to the Good Folks of Stockton'. The tune prescribed was 'Push about the Jorum'.

It would be tedious to type it all out, but fortunately a facsimile can be seen at The Farne Archive.

The site is designed so that it is impossible to link to materials externally; run a search there for yorkshire volunteers and you will find it.

The original tune can be found quite easily via google; I don't know if Vin Garbutt used it or something else, though.