Reviving an old thread.

Whitby Abbey was wrecked by Henry VIII in 1540

There's no reason to think the song is that old, or that it has anything to do with the monks.

On the contrary, there is good reason to think that the song is quite possibly that old. See the information in the Yorkshire Garland Link above.

OTOH, It may not have much to do with monks as the old coffin routes were used by lay people to carry the coffins to consecrated ground for burial.