There's also a lot of Anglo Saxon, French and other European influence on place names and architecture. But to call that Celtic (even though the Celts may have come from Europe many centuries back) isn't useful to someone who's trying to distinguish modern "Celtic" music (much of which is as artificial as the Waterson/Carthy stuff you keep on about, by the way) from "English" folk music.

What about the rigid stylised requirements of the Welsh eisteddfodau? or the equally rigorous formalities and rules of the Royal Scottish Country Dancing Society? Is that celtic? it certainly isn't English. Does it count? who gets to choose? It's dangerous to generalise.

Anahata