Barry Cunliffe gives an informative lecture to an American audience in this video from 2008.
He discusses older theories regarding the Celts, who they were and where they came from before discussing current ideas as of the date of the lecture.
His conclusion is that the evidence so far shows that the Celts didn't come here but were rather here before spreading out into various parts of Europe. He shows them at the heart of an Atlantic trading 'empire' along the coast of western Europe from Spain and Portugal in the south to possibly Denmark in the north.
He seems to put forward that the Celtic language of the time was probably a trading language understood by such diverse peoples although he does touch on dna evidence showing a possible origin in Iberia.
https://www.youtube.com/watch?v=G8FM9nMFbfIFor those interested here's the link. For those not interested please feel free to harrumph.