I can't see why anyone should cite Lonnie Donnegan as a significant impact on the present shape of folk music in the UK (ok, I do know the arguments behind that claim; I just don't agree with the conclusion drawn) I'm delighted to celebrate Carthy.
He, himself, would never exagerate his influence. And would certainly place himself in the "second wave" of the revival, behind Bert Lloyd, Ewan MacColl, etc (I was even more puzzled by the contributor who elevated MacColl above Lloyd in the chronology of UK folk). I've not met anyone more ready to acknowledge his sources, and to play down his own influence. Yet I agree with Ed - Carthy's position is unique, and distinct from others of the same generation who have been named here. Justly recognised by his MBE, which - typically - he takes as recognition of his music and his "roots" rather than as a purely personal honour.
But important to CELTIC music?? There must be some mistake!