In 1965 the performance artist and experimentally-minded musician Yoko Ono was sat on stage at Carnegie Hall. She was wearing her best clothes – who doesn’t want to look good when playing Carnegie Hall? – and in front of her, positioned on the floor like a question mark left hanging, was a pair of scissors. Ono had performed her Cut Piece previously in her native Japan, but it was this New York performance that captured imaginations. Audience members were invited to come up on stage, single file please, and cut off small pieces of her clothing which they could take home as a memento. And Ono remained motionless throughout, calling time on the performance only to protect her increasingly fragile dignity.

Cut Piece encapsulates all that has remained puzzling and intriguing about Yoko Ono’s art; file under 4’33”, headlining quackery that is destined to be misunderstood and misrepresented. It places Ono in a time and place before she met, and then in 1969 married John Lennon, just as The Beatles were preparing to crash and burn. I’ve no doubt that our perspective on Ono’s artistic achievements would be utterly different had she somehow managed to avoid marrying Lennon. As things stand though, especially given the circumstances of his tragic death, Ono has become an inseparable part of the Fab Four mythology, and a troubling part at that. Because, despite all the evidence pointing to a more nuanced and complex story, Ono remains the femme fatale whose actions, apparently, led to the unthinkable breakup of The Beatles.

It was Ono who dragged Lennon to New York City, insisting that they move into a chic apartment block on the Upper West Side just along the corridor from the Bernstein residence, and pumped his head with pretentious, conceptual bull. It was Ono who Paul McCartney distrusted. Cue a feeding frenzy of tabloid tales, the idea that Ono had had an independent creative life before Lennon conveniently airbrushed away.

Celebrity operates under its own rubric, and paradoxically, as Ono’s work was being eclipsed by her association with Lennon, that same association handed her a platform and visibility she would have been unlikely to achieve under her own steam. And without those affiliations, that reflected Beatles glory – celebrity doesn’t come any grander – it’s doubtful that Ono would now be acting as guest director of the Southbank’s 2013 Meltdown festival, which opens this evening with a performance by the Yoko Ono Plastic Ono Band. On the rebound from the festival’s early days when the likes of George Benjamin, Louis Andriessen and Magnus Lindberg programmed what was essentially a New Music festival – which presumably didn’t sell enough tickets – Meltdown has cannily repositioned itself as a celebration of artsy rock music, featuring guest artistic directors like Jarvis Cocker, Patti Smith, Laurie Anderson and Robert Wyatt whose music has, at the very least, been informed by wider notions of modernism: jazz, minimalism, electronics, alt folk, conceptual art. Intelligentsia pop for adults. Meltdown directors are instinctive underground thinkers who have a knack for dragging their message towards mainstream consciousness where, even if not fully grasped, their theories of the world are at least discussed.

Yoko Ono fits that brief completely. Looking through the Meltdown programme, though, you can’t help but regret the compromise of selective history, a golden opportunity to portray her story in the round largely squandered.

In the mid-1950s, when Ono came to New York she gravitated towards John Cage and proto-minimalist La Monte Young, and married a former Cage pupil, the composer Toshi Ichiyanagi. Her Tribeca loft space evolved into a hub for ‘happenings’ and performance art, and subsequently she became linked with George Maciunas’s Fluxus movement, Dadaist ideals reformatted for the modern age. Now Cage is gone and concert hall remakes of free-spirited 1960s happenings tend to be stiff and inauthentic travesties. Fair enough. But the 2012 release on the EM label of archival material recorded during a 1962 Cage/Ono Japanese tour – Ono’s impressively furious and corporeal vocalising heard on a realisation of Cage’s Aria and Solo for Piano with Fontana Mix – reminds us how artistically bonded they were. But what a pity that, down among all those Meltdown concerts by box office certs like Boy George, Iggy Pop and Patti Smith (no slight intended, I’d pay good money to see them all), the only hint of this early experimental vein is Sky Piece for Jesus Christ in which an orchestra tries to play while their limbs are bound with fabric. That same old same old image of Ono as Mrs John Lennon is left unquestioned.

And then there’s Cut Piece, to be performed by Canadian popster Peaches. The problem with this onetime sincere piece of performance art is that now we know too much. Back in the day, Ono was clear about her intent: artists need to be stripped of ego, they must keep their artistic commitment under constant review. Cut Piece was a cleansing ritual, artistic purity reduced to its naked, vulnerable essence. And I totally get that, in 1965 at America’s most august classical music venue, the sight of this dignified young Japanese woman handing herself over to an audience of complete strangers had a potent symbolism.

But now we really do know far too much. Together, Ono and Lennon were capable of monstrous displays of self-regarding rock star-ego baloney. 'Imagine' – written by Lennon, produced by Ono – and not, as is often assumed, a Beatles song – is an unpalatably mawkish and crass ditty by a once thoughtful songwriter besotted with his own charisma; a messianic rock star worth gazillions, lording it up in the Dakota Building, has a problem with material possessions. The trajectory from Cut Piece to 'Imagine' says it all.

And after Lennon’s murder, Ono refracted her early work through rather nebulous, ill-defined ideas of world peace and humanitarianism honed while he was still alive. When she performed Cut Piece in 2003, it was now about peace and – why not go for a full suit of worthy causes? – also aimed against racism, sexism and violence. No doubt that some of the hatred aimed towards Ono by Beatles-bores certain of her malign influence was motivated by racism and sexism. And anyone from Japan, of course, has peculiarly painful memories of the apocalyptic aftermath of war. But performance art, by definition, preaches to the converted. It’s a blunt political tool that never changed anything. Which doesn’t mean it’s not worth doing. Far from it. But self-awareness and humility need to be your watchwords.

Ono’s strongest work musically has been with her Plastic Ono Band, the envelope name she has lent to a number of live and recorded projects that, over the years, have drawn on a pool of musicians including Eric Clapton, Phil Spector, Klaus Voorman and Keith Moon. And it’s entirely fitting that two Plastic Band performances bookend Ono’s Meltdown. The eponymous 1970 debut Plastic Band release is a curious kind of masterpiece. The Ornette Coleman Trio turn up on one track (killer fact: this track was recorded two years earlier than the rest of the album when Ono came to London with Lennon; and as Yoko recorded with Ornette, The Beatles cut 'Lady Madonna', with a riff quite obviously pilfered from Humphrey Lyttelton’s 'Bad Penny Blues') while the rest is an artfully assembled montage of musique concrète, vocal sounds and studio wizardry. 'Paper Shoes' shows just how sharp Ono’s ears could be. Listen to the sounds, forget the ego.

Yoko Ono's Meltdown Festival starts tonight (June 14) at London's Southbank Centre and continues until June 23. Click here for further information