This was a typical warrior elite sort of thing, they owned boats and engaged in both raiding and trade (selling what you steal is the only way to keep the boats afloat).
That was about 1000 BC.
They sailed around the Mediterraean for a few centuries ~ built some fortified towns ~ finally abandoned the area and settled in NW Spain in roughly 700 BC. They gradually took over adjoining Basque areas and finally took off for Ireland and Britain in maybe 500 BC. They took the Basques with them.
Again, they never got out of the warrior elite thing so their genes just disappeared in the far greater Basque and native Celtic genepool, but they did dominate with their language(s).
By the time the Romans arrived in 35AD the Irish were sufficiently advance to be too expensive to be conquered and dealt with. The Celts in Wales were also too expensive to be dealt with. The Celts in the Southern Coastal areas had the best lands and the Romans took them ~ see Boaddica ~ whose name is in a language that's probably been extinct about 1600 years ~ but it says she's the 'feminine form" King Arthur ~ which is really cute. Kind of different than the story handed down by the Romans but it doesn't seem to bother any of the old Celtic language specialists.
The Galician story is gradually displacing the competing British theories.
About 535 AD all he-double toothpicks broke loose and a large number of folks from SE Britain, and Cornwall, moved to Brittany ~ which had just recently lost all its population, its covering vegetation and its wild animals, so it was a mess.
BTW, Brittany in Roman times was run independently of Rome for some reason. These are the same people who'd earlier been allied with Carthage but I suspect they made a separate peace with Rome and that gave them a special status.
The more recent and significant history after the withdrawal of the Legions from Britain is simply that of Brittany ~ which worked in tandem with its counterpart Cornwall to control trade between the mediterranean and the North Sea. They became incredibly wealthy during the early Medieval period, and that lasted right down to Anne of Brittany who was married to three French kings among other things and was reputed to be the richest woman in Europe. The French royal family married into Brittany's top nobility and gradually took over.
I'd say that the first caused the second. Meaning that Rome had to either conquer Ireland, or leave the Britons in what is now Wales enough of their ancient tribal structures, and enough personal pride, and enough arms, to protect themselves from Irish raiders. Rome could not reduce them to sullen, unorganized, unarmed, sheep, as it did to the inhabitants in most of the Western Empire, without first eliminating the Irish wolves just to the West.
But Rome did conquer them, although it did not oppress them to the same extent it did in the areas of Britain nearest Gual. The oldest continuously existing Christian community in the British Isles is in Wales. The very name "Wales" comes from the name for foreigner that the Germanic barbarians gave to to people and things assciated with Rome. Wallonia, Wallachia, Vlach, walnut and Wales all derive from the same Germanic root word, because the Germanic invaders of Britain associated the Christian people of what we now call Wales, whose priests and ruling class could speak Latin, with Rome.