Alleluia! Sing for joy and celebrate - tune origin

This is a round (entitled "Jesus, Jesus") whose tune looks to me an awful lot like "Heigh ho, nobody home / Meat nor drink nor money have I none". It's attributed to Ravenscroft, and I'm looking for more specific attribution, i.e. (a) did Ravenscroft compose it or did he collect it — he was a major collector of rounds and similar simple folk tunes in the early 17th century — and (b) in which of his works does it appear?

I've put a thread on this on the Mudcat Café, here, if anyone knows anything feel free to post it either place...