Celts are not indigenous to the British isles. They were another Indo-European group that came from Germany. When Julius Caesar invaded Britain, he met Celtic tribes in SE Britain who still remembered coming from Northern Europe. He also met a more ancient race in the interior who believed that they had always lived in Britain. These first Britons were probably related to the Basques a non Indo-European group.
The Celts got around. I was reading a book on China, and apparently they have some mummy discoveries from the western part of the country that appear to be Celts, with plaid clothes, even.
As far as oral traditions and archeology go, it seems that the Celts arrived in Britain in several waves, the first one being about 4500 BC, a second really big one about 2500 BC. The aboriginal inhabitants were of Hamitic stock and probably came from North Africa/Middle East sort of area.
Yeah, but why should the BBC let a little thing like that get in the way of an anti-English narrative