We're nearly all Celts under the skin
Instead, a research team at Oxford University has found the majority of Britons are Celts descended from Spanish tribes who began arriving about 7,000 years ago.
Even in England, about 64 per cent of people are descended from these Celts, outnumbering the descendants of Anglo- Saxons by about three to one.
Previously it was thought that ancient Britons were Celts who came from central Europe, but the genetic connection to populations in Spain provides a scientific basis for part of the ancient Scots' origin myth.
The Declaration of Arbroath of 1320, following the War of Independence against England, tells how the Scots arrived in Scotland after they had "dwelt for a long course of time in Spain among the most savage tribes".
Professor Bryan Sykes, a human geneticist at Oxford, said the myth may have been a "residue" in people's memories of the real journey, but added that the majority of people in England were the descendants of the same people who sailed across the Bay of Biscay.
Prof Sykes divided the population into several groups or clans: Oisin for the Celts; Wodan for Anglo-Saxons and Danish Vikings; Sigurd for Norse Vikings; Eshu for people who share genetic links with people such as the Berbers of North Africa; and Re for a farming people who spread to Europe from the Middle East.
The study linked the male Y-chromosome to the birthplace of paternal grandfathers to try to establish a historic distribution pattern. Prof Sykes, a member of the Oisin clan, said the Celts had remained predominant in Britain despite waves of further migration.
"The overlay of Vikings, Saxons and so on is 20 per cent at most. That's even in those parts of England that are nearest to the Continent," he said.
"The only exception is Orkney and Shetland, where roughly 40 per cent are of Viking ancestry."
In Scotland, the majority of people are not actually Scots, but Picts. Even in Argyll, the stronghold of the Irish Scots, two-thirds of members of the Oisin clan are Pictish Celts.
However, according to the study, the Picts, like the Scots, originally came from Spain.
"If one thinks that the English are genetically different from the Scots, Irish and Welsh, that's entirely wrong," he said.
"In the 19th century, the idea of Anglo-Saxon superiority was very widespread. At the moment, there is a resurgence of Celtic identity, which had been trampled on. It's very vibrant and obvious at the moment.
"Basically the cornerstone of Celtic identity is that they are not English. However, to try to base that, as some do, on an idea that is not far beneath the surface that Celtic countries are somehow descended from a race of Celts, which the English are not, is not right. We are all descended from the same people.
"It should dispel any idea of trying to base what is a cultural identity on a genetic difference, because there really isn't one."