I'm surprised that no body has yet mentioned the work of Martin Carthy, Norma Waterson and Eliza Carthy! All three family members are widly known for playing largely English music. Martin Carthy is also a sometime member of Steeleye Span (early days), and with Norma, involved in The Watersons.
As far as other major modern performers of English folk music goes, you could also try looking for (in no particular order): John Kirkpatrick (melodeon, accordion, Anglo concertina and voice), The Albion Band, Kate Rusby (guitar and voice), Nancy Kerr (fiddle and voice), Nic Jones (guitar and voice) and Shirley and Dolly Collins (voice and various keyboard instruments). I've only mentioned a few that I hope will be fairly readily available in America.
As far as source recordings go, the Voice of the People series on Topic Records is a very good place to begin. Also recently issued is Absolutely Classic, an album of William Kimber's concertina playing, on EFDSS recordings. (He was a member of Heddington Quarry Morris Dancers at the end of the last century, beginning of this century, and has been highly influencencial for a lot of people.)
Hope that's helpful.