Does anyone know the origin of the song Barnet Fair as sung by Steeleye Span https://www.youtube.com/watch?v=p9DyIpbMJx0?

I know about Barnet Fair itself (I was born in Barnet) but is the song traditional or written by Steeleye (or someone else)?

I can only find Steeleye's version so I suspect it was written by one or more of them.