Not sure if these count:
Shirley Collins with David Munrow's Early Music Consort of London. Although a folky, Shirley would be involved with the early folk-rock Albion Bands (even marrying bass player Ashley Hutchings who was also a founder of Fairport and Steeleye Span). In fact the various mutations of the Albion band regularly mixed rock beats with elements of early music with Phil Pickett, who had another life as an early music specialist, often aboard (he also guested on many a Richard Thompson record).
And on the same lines, a band called Gryphon with a liking for crumhorns and the like.