'Come Haste to the Wedding' appeared as a song in The Elopement (Drury Lane, 1767, according to Chappell, English National Airs, 1840, no. 163). See Journal of the English Folk Dance and Song Society, III, 3, 1938, 208-210, for background and some speculation on the subject.

Broadside examples at  Bodleian Library Broadside Ballads:

Come Haste to the Wedding

There is also a text, apparently taken from a modern arrangement, in the DT:  HASTE TO THE WEDDING (Rural Felicity): contains the unexplained comment 'Collected from Eunice Carew's songbook, 1790'.

The tune (as opposed to the song) has been claimed as both Irish and Scottish; Bruce Olson reckoned that the earliest known example was the Scottish 'The Small Pin Cushion'. I expect you already know that.