Probably the one kind of 'English music' that is nearest to what you call 'Celtic Music' is Northumbrian music. The people of the North-East of England didn't throw their music away in the same way as many of the other parts of the country. You could start with than fine piper, fiddler and composer Kathryn Tickell.

weelittledrummer thinks that English music was imported from Ireland and Scotland - there's no evidence for this, more of a shared culture that the English disregard more than did their neighbours. But then he thinks the Watersons are middle-class! Check out their (non-middleclass) work as Waterson:Carthy and particularly the work of Eliza Carthy who has done more than most to re-introduce English instrumental music. And its not twiddley-dee and morris prancing as GUEST,Red thinks (I always value an opinion based on widespread knowledge and pure science). Jigs have been around England Ireland and Scotland for a long time, and it would not be possible to say who got them first.

John Kirkpatrick has been a strong supporter of English music for many years - check out the many things he's been involved in. And if he can march to anything he plays he's even cleverer than I thought he was and I'm going to count his legs again next time I see him.