As a sailor, for me it's more likely that the Basques arrived in Iberia from the British Isles than the other way about. Prevailing winds and surface currents in summer all tend to try to throw anything leaving the Cantabrian coast straight back onto it.
Also if you read up on the tin trade in Cornwall the Britons went to quite some trouble to make sure foreign merchants never saw the mines or the settlements of the miners, indicating they were on the whole quite an insular bunch. If they'd been that way since the channel flooded some 8 to 10 thousand years before it's likely they were culturally quite different to the continental Celts.
As for what they looked like, they were reported to be blond or red haired with large moustaches. Like this?
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