He's the epitome of the heroic Celt, the embodiment of Ireland's mythic past in the public imagination. Long hair flowing from under his helmet, spear and shield in hand, Cúchulainn fearlessly rides into battle on a chariot embellished with interlaced motifs. For more than a century this has been the popular image of Celtic culture. And we may owe it all to Theodore Roosevelt.

Long interested in the myths of Ireland, the US president wrote an essay on ancient Irish sagas for the Century magazine in 1907. The article was accompanied by a striking illustration of Cúchulainn by the American artist JC Leyendecker, which featured all the elements that have since become associated with the Ulster Cycle's hero.

"Within a year, versions of Leyendecker's portrait of Cúchulainn could be found in any number of penny pamphlets in Ireland, promoting the idea of heroic Irish sacrifice in many nationalist circles," says John Waddell, professor emeritus of archeology at NUI Galway and author of the recent study Archaeology and Celtic Myth. "So the Celtic warrior myth fed into all sorts of things, good and bad."

As well as providing mythological inspiration for the likes of Patrick Pearse, Cúchulainn would feature in pop-art posters, rock concept albums, republican and loyalist murals and superhero comics. All of these drew on the template forged by Roosevelt's illustrator.

Above all else, the diverse manifestations of the Cúchulainn myth underline not so much its enduring appeal as its cultural malleability.

Much the same could be said about the ancient Celts themselves, and their legacy. Two and a half thousand years after a group of peoples linked by art and, most likely, language emerged in the lands north of the classical Mediterranean civilisation, the Celts continue to exert a powerful influence.

These days the diversity and distinctiveness of this vibrant heritage are being showcased beyond the so-called Celtic fringe heartlands – Ireland, Scotland, Wales, the Isle of Man, Cornwall and Brittany – and raising contentious questions about the Celts’ origins and about Ireland’s traditional self-image as the primary guardian of the Celtic flame.

Celtic culture, ancient and modern, is the subject of a major exhibition at the British Museum, in London. Celts: Art and Identity highlights the diversity of this artistic legacy while subverting some popular misconceptions, most notably the notion that the Iron Age people were a single migratory race from whom the Irish, and their Scottish and Welsh cousins, are descended.

"The story we are telling isn't the conventional story of a single people or ethnic group," says Dr Julia Farley, curator of the exhibition. "We're really telling the story of a name, a label, and how it has been reinvented over that incredibly long period of time."

The term Celt was originally used by the ancient Greeks and, later, the Romans, to describe the people who lived to their north who adopted the figurative artistic styles of the classical civilisations into the distinctively abstract forms we now know as Celtic art. This common style, along with certain linguistic and religious traits, linked the Celts across Europe. “We’re looking at a very connected Europe in this story,” says Farley.

Language versus genetics

A couple of millenniums later the phrase was resurrected as a unifying term for the interlinked Irish, Scots Gaelic and Welsh languages and the people who spoke them. But the British Museum show makes clear that there is virtually no racial connection between the ancient Celts and the nations that now identify themselves as such.

"They're two totally different elements," says Ned Kelly, a former keeper of Irish antiquities at the National Museum of Ireland. "Because people have placed the label Celtic on all of these things they assume they're all the same. But they're not. If our Celticity is determined by the fact that we speak a particular language that has been defined by linguists as Celtic, then we are Celts. But if one is suggesting that we are genetically related to the peoples of central Europe who spread out here in the Iron Age, then there isn't a shred of evidence for that."

It’s easy to see how this confusion arose. While Celtic design faded in Britain after the Romans invaded, in unconquered Ireland the style mingled with Anglo-Saxon and even Christian influences and survived in new forms. Pieces such as the Tara Brooch, the Ardagh Chalice and the Book of Kells were produced long after the Iron Age yet contain what Waddell calls “definite remnants of the old glories” in their motifs.

Then, in the 19th century, this artistic legacy combined with our comparative geographical isolation and troubled relations with Britain, and the idea of a separate Celtic identity took shape in Ireland.

“The term Celtic is in part a reaction to the concept of Britishness. It’s a nationalistic response,” says Kelly. “We were being lumped in as British after the Act of Union, and the Irish always thought of themselves as a nation apart.”

Waddell agrees. “It does shape our world view and how we view our neighbours. They perhaps lack our sense of identity, and we maybe have too much.”

Although there was a resurgence of interest in ancient Celtic culture across much of Britain in the Victorian age, the effect of this movement was largely felt on the arts and crafts of the era (particularly in Scotland) or in the rise of druidic cults and mysticism. In Ireland it underlined a rising nationalism and cultural differentiation.

Irish mythology, as revived and popularised by WB Yeats and Lady Gregory and championed by President Roosevelt, was particularly important. These stirring tales of heroes sacrificing themselves against the odds struck a chord with the wider mood. That such tales were particularly Irish rather than generally Celtic was beside the point, as the two terms were conflated; after all, we still talk about the time as the Celtic Revival.

Pearse’s sacrificial gesture

This development arguably reached its apotheosis with the heroically sacrificial gesture that Pearse made in the name of Irish freedom during Easter week 1916. It was a particularly Irish twist on the nationalist movements that emerged throughout the 19th century and found appalling expression in the Great War.

“Archeology and language merged to produce an image of the Irish as racially distinct,” says Waddell, “but, as elsewhere, the situation was simplified in a pretty ghastly way.”

But after the establishment of a independent Irish state this Celtic sense of identity took a back seat to a more explicitly Catholic ideology. That Flann O'Brien's gently subversive masterpiece At Swim-Two-Birds features disgruntled figures from Irish mythology coming to life to escape the feckless author's narrative is an apt metaphor for recently rampant Celtic passions straining under Free State piety.

In the early 1970s newfound prosperity, increased social freedom and resurgent unrest in the North started to overturn the old certainties of Irish life. The artist Jim Fitzpatrick turned to ancient myths and Celtic motifs to produce vivid, comic-book-tinged posters whose pagan wildness chimed with the counterculture of the era.

Fitzpatrick's art evoked a country in touch with its pagan past yet free of the constricting shibboleths of the church: his cover for Thin Lizzy's 1976 album Johnny the Fox looks like a pop-art take on an illuminated manuscript.

Another Irish rock group, Horslips, were more explicit in their Celtic references. At a time when nationalism and unionism were colliding in the Troubles, the band set Irish myths to a driving folk-rock sound on albums such as The Táin – which told the tale of Cúchulainn – and The Book of Invasions, which was subtitled A Celtic Symphony.

Their "Celtic rock" proved hugely popular with audiences throughout Ireland in the 1970s, their appeal even crossing the sectarian divide in the North. (Full disclosure: Barry Devlin, the band's bassist, is my uncle.) Celtic culture could be embraced by all, as underlined by those loyalist murals claiming Cúchulainn as a defender of Ulster.

If Celtic culture took on a more benign quality in Ireland, it was more divisive in some quarters. During the second World War a paramilitary group of Breton nationalists called Bezen Perrot, who made much of the Celtic origins of their native language, operated under the auspices of the SS in Nazi-occupied France. After the war one former member, Louis Feutren, moved to Ireland, where he taught French.

After he died, in 2009, Celtic-studies departments in universities in Wales and Brittany spurned donations from his estate. (As a former pupil of Feutren I can attest that he never hid the fact that he fought under SS command.)

Meanwhile, in certain far-right circles, the Celtic cross has become a pernicious signifier of racial purity, adding another sinister layer of ambivalence to a cultural legacy that has thrived on adaptability down the centuries.

Although Scotland has a rich heritage of artefacts and a language that shares much with Irish – the British Museum show is jointly organised with National Museums Scotland – the term Celtic has often been problematic there. It is telling, for instance, that Glasgow Celtic has traditionally been the team of Scotland’s urban Irish Catholic minority, while Farley suggests that people in the Scottish highlands have been more likely to call themselves Celts. “The word Scottish is something unifying, whereas Celtic can be seen as divisive,” Farley says.

Such themes are not explored in detail at the British Museum; even the Celtic Revival gets comparatively short shrift. (Indeed, this modern legacy was elided completely from the recent BBC television history series The Celts: Blood, Iron and Sacrifice.) Instead the London exhibition focuses on the notion that, as Farley suggest, Celticity is "a cultural rather than an ethnic identity", displaying flagons from Lorraine and giant cauldrons from Denmark.

There are still significant differences of emphasis between British and Irish archeologists. The British Museum catalogue remarks that there was no single language; this glosses over the fact that there was a “language family that facilitated communication and shared belief systems”, says Waddell, who likewise disagrees with the “old canard” that the ancient Celts did not use that word to describe themselves.

The problem may just be the word Celtic, with its multitude of meanings and loaded associations. “I think we’re stuck with it now,” says Kelly. “But in the popular imagination, and in popular music, it does have a certain validity.” Sure enough, folk music in Ireland, Scotland, Brittany and the Spanish region of Galicia (which increasingly identifies as Celtic) enjoys rich cross-pollination.

In the end what constitutes Celtic culture may depend on one’s perspective. From a British point of view the Celts can be seen as a unifying, pan-European force. “I don’t think you can separate the story of our small islands from the bigger picture of which they form part,” says Farley. For the Irish such a view risks recasting the continuities of ancient Celtic art and the linguistic communities of the Atlantic coastal nations as an Iron Age trading bloc that somehow ended up as an accidental culture. For a civilisation that supposedly brought people together, the Celts can still provoke divided opinions.

Celts: Art and Identity is at the British Museum, in London, until January 31st