Memory is a great maker of fictions. Take the 1960s. The decade exists in the public imagination in a quite different way from the one most people actually lived through. The old line goes that if you can remember the 60s you weren’t there, but it’s probably more truthful to say – you were there, only you didn’t hang out in Carnaby Street, have your clothes made by Mr Fish or trip on acid while driving a Lotus Elan. You didn’t swing. But there was something infectious in the air all the same, something in the decade’s high summer of 1967 that smacked irresistibly of a burgeoning freedom and revolt. Maybe it was the news that homosexuality had been decriminalised, or hearing the Beatles’ “A Day in the Life” for the first time, or the unprecedented glimpse of pubic hair in that film at the Odeon. What was its name again?

The film was Blow-Up, and 50 years after its UK release it reverberates way beyond the notoriety of Jane Birkin showing her bits on screen. Appropriately for a picture about perception and ambiguity, it plays very differently from the one I remember first seeing years ago – I could have sworn it was in black and white, for a start. It marked a departure from director Michelangelo Antonioni’s previous studies in alienation, most notably La Notte, in which Jeanne Moreau wanders lonely about the streets of Milan while the beautiful people party on in listless defiance of boredom.

Blow-Up, his first English-language production, dives head-first into swinging London, seen from behind the wheel of a dandy photographer’s Rolls convertible – already, younger readers will be thinking of Austin Powers – as he bounces from slumming in a dosshouse to cavorting with dolly birds and models in his studio. There is a reason Antonioni has made the protagonist a photographer – a man who looks but doesn’t see – just as there was for replacing his original actor, Terence Stamp, with the relatively unknown David Hemmings.

But the film has something else Antonioni had never deigned to include before: a story. An oblique and maddening one, for sure, but a story nonetheless. The photographer, fed up with the birds and the mod fashion shoots, goes off in search of fresh air – and fresh mischief. He finds himself in a park, where the breeze sounds in the tops of the trees like the sea at low tide. In the distance, he sees a man and a woman, together, canoodling. He points his camera and takes a few snaps of them. On his way out, the woman (Vanessa Redgrave) chases after him and demands, urgently, that he hands over the film. He refuses. She tracks him back to his studio where they smooch, smoke a joint, play some music – and he sends her away with the wrong roll.

‘The same patient build-up, the same slow-motion shock’ … a frame from Abraham Zapruder’s film of the Kennedy assassination. Photograph: James W Ike Altgens/AP

And here is where the film unfolds its most brilliant and memorable sequence, the part you want to watch over and over again. Alone in his dark room, our hero blows up the photos from the park and discovers that he may have recorded something other than a tryst. Cutting between the photographer and his pictures, Antonioni nudges us ever closer until we see the blow-ups as arrangements of light and shadow, a pointillistic swarm of dots and blots that may reveal a gunman in the bushes, and a body lying on the ground. Has he accidentally photographed a murder?

Contemporary audiences watching the way Thomas, the photographer, storyboards his grainy images into “evidence” would surely have been reminded of Zapruder’s film of the Kennedy assassination in 1963: the same patient build-up, the same slow-motion shock. When Thomas returns to the park he does indeed find a corpse. It’s the grassy knoll moment. We feel both his confusion and his excitement at turning detective – he’s involved in serious work at last instead of debauching his talent on advertising and fashion. But, abruptly, his investigative work goes up in smoke.

Next morning, the photographs and the body have disappeared. The woman has gone, too. This links to larger fears of conspiracy, a sense that shadowy organisations are hovering in the background, covering up their crimes – and getting away with it.

Blow-Up looks back to Zapruder but also ahead to Watergate and a run of films that riffed in a similar manner to Antonioni, with his inquiring, cold-eyed lens: Gene Hackman, stealing privacy for a living as the surveillance genius in The Conversation (1974); witness elimination and the training of assassins by a corporation in The Parallax View (1974); later still, Brian de Palma’s homage to the sequence via John Travolta’s sound engineer in the near-namesake Blow Out (1981). But these sinister implications are not on the director’s mind. Where we anticipate a murder mystery, Antonioni balks us by posing a philosophical conundrum. “It is not about man’s relationship with man,” he said in an interview at the time, “it is about man’s relationship with reality.”

Having created the suspense, he declines to see it through and sends Thomas off on an enigmatic nocturnal wander – to a party where he gets stoned, to a nightclub full of zombified youth where, bafflingly, he makes off with a broken guitar. (The film’s other symbolic artefact is an aeroplane propeller he buys in an antique shop). Finally, and famously, he encounters a bunch of mime-faced rag-week students acting “crazy” and playing a game of imaginary tennis on an empty court. We even hear the thock of the tennis ball, though there isn’t one in sight. Antonioni seems to offer only a shrug: reality, illusion, who can tell the difference? Whenever I watch Blow-Up, I feel a sense of anticlimax, of a road not just missed, but refused. Yet as much as it irritates, it still intrigues, and asks a question that relates not merely to cinema but to any work of art: can we enjoy something even if we don’t “get” it?

Blow-Up has great things in it – Hemmings’s insolent gaze, how he throws himself across the floor to reach the phone

It’s a question discussed by a mother and daughter in my new novel, Eureka, on seeing the film in the week of its Uk release, in March 1967. Eureka itself is about the making of a mystery film in London, not another Blow-Up, but an adaptation of Henry James’s short story “The Figure in the Carpet”: two friends revere an ageing novelist, who tells one of them that no reader has ever located the elusive secret of his work, “the string the pearls were strung on, the buried treasure, the figure in the carpet”. The friends’ efforts to discover what it is becomes an increasingly fraught and bitter contest. The screenplay is interspersed between the story’s chapters.

Reviews of Blow-Up at the time gave it a guarded welcome. Penelope Houston in the Spectator called it a failure “for which I would trade 10 successes”. Dilys Powell reckoned Antonioni’s cinema “beautiful and difficult”, and suggested that his films might become “even stranger and more exciting”. Not many would agree that they did. What might have been a turning point led only to a cul-de-sac. Vagueness and obfuscation hardened into a style. Zabriskie Point (1970), his meditation on America, is a lowering, vacuous mess. The Passenger (1975), about another disappearing act, had its fans, though Kenneth Tynan wasn’t one of them: “Maria Schneider and Jack Nicholson are under-directed to the point of extinction. One doesn’t mind (one can even tolerate) bad acting: but slow bad acting is insupportable.” There is something terribly dismal in his vision of humankind, and terribly humourless. Few major filmmakers have shown so little faith in story.

But Blow-Up, flawed as it is, can still thrill us 50 years on. It has great things in it – Hemmings’s insolent blue gaze, and the daft way he throws himself across the floor to reach the phone; the wind soughing through the trees in the park; the busy jazz score by Herbie Hancock; the unsettling charm of those London streets. And, in the sequence from which it takes its title, that rapt attention to the photographer’s art really is something to behold.

• Eureka by Anthony Quinn is published by Jonathan Cape on 6 July. To order a copy for £11.04 (RRP £12.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.