As I grew up I admired the Celts and aspired to be one. They coloured my reading up to the age of ten or so, but as I headed towards twelve and thirteen I began to suspect that all was not as it seemed. Instead of the brave, heroic characters I'd read about, I began to see the Celts described as war-mad and quick to battle, a race that inhabited most of Europe and described as barbarians. It was suggested that they were the barbarian hordes who poured into Europe from the Asiatic plains. They seemed to be essentially nomadic, and warlike, liked alcohol and imbibed rather too much, and fought naked - something I've always found hard to believe when Men are so precious about their bits they refer to them as "the crown jewels."
Then the picture of naked wild people rushing into battle began to change. Ceasar was impressed by tribal groups in Gaul with towns and stable government, Druids went to Rome and gained respect, but then there is a huge chunk of time when Celtic peoples and things sank into obscurity. Not until the linguist Edward Lhuyd published Archaeologia Britannica in 1707 were the languages of Ireland, Scotland, Wales, Cornwall and Brittany recognised as belonging to the same family and lumped together under the name Celtic. He too speculated the peoples had moved into Britain from central Europe.
From the mid-1960s, evidence began to refute such claims and a new theory was formed: the "Celtic" languages were a common language family that fronted the Atlantic coast from the fifth century onward. Ceasar said that the land between the rivers Seine and Garonne in France (think of the city of Bodeaux, on the Garonne) was known as Celtica. There is no mention of any ancient writer referring to the Britons as Celts. The island was known as the isle of the Albiones and Ireland inhabited by the Hierni, though the more popular name was Prettanika or Pretannia. Prettanika may come from the term "painted peoples" but was not used by the people themselves; it was more likely the people of Gaul who used the term of the people who lived in Pretannia.
It would seem the inhabitants of the islands were not immigrants, but indigenous peoples who shared their culture along the seaways with their continental neighbours. This superficial description of ongoing research can easily be explored in much more depth by tacking papers written by people like Barry Cunliffe, emeritus professor of European Archaeology at the University of Oxford. He wrote Britain Begins (OUP, 2013)