Technically you're right, Beale. But realisticaly Celt has now got a new meaning, and is very firmly attached to the Welsh, Cornish, Irish, Breton and Scots cultures of NW Europe -- whatever their origins. They do all share a common language family, and what else are you going to call that?
Incidentally, the origin of the language and culture is thought to be somewhat independent from the blood-descent -- so many English" people are probably largely "Celtic" by blood, and Welsh people are quite likely to be mainly "pre-Celt". Everyone is mixed up really...
Allie1234cat -- The Picts were Scotland, not Wales, and I'm not even sure if they were Celts at all.
Cymru am Byth, too (and yes, that's correctly spelt).