Most of the pejoratised Folk Rockers were in fact folkies of some sort anyway. I seem to remember Martin Carthy in Steeleye Span, for instance!

And Steeleye Span (and Mike Batt) effectively DID write "All Around my Hat", as it's a conflation of at least two totally different songs and maybe a third tune. They did a similar trick with "The Weaver and the Factory Maid". As did Nic Jones, Swarb, Mr. Carthy, Bert Lloyd, Ewan MacColl, Uncle Tom Cobley etc.