Guest, "Jones" is not a Celtic name, although it is common in Wales. I am not "celtic", whatever that means.

The "English" did not "invade" these islands. Since the last ice age there has been as steady migration westwards. A number of peoples from Western Europe migrated into the British Isles over a lengthy period. No doubt this involved a certain amount of conflict, but your implication of a co-ordinated military takeover which evicted the native celts is pure fantasy. Anyway, the Britons in their turn had been part of an earlier migration. Over a period of centuries, which included further immigration from Scandinavia and Normandy (which was a Viking outpost)these peoples developed into what we now call "English", and their kingdoms merged to become England.

No doubt these peoples brought their own traditions with them. It is very unlikely they bore any resemblance to what we currently think of as English traditional music, any more than modern Irish trad can be traced back to the music of the Ancient Britons. Both are developments of the last few hundred years only.