Of course I feel a bit silly. I am standing in a gallery gazing at a blow-up plastic dolphin. And why would anyone do that — not least when there’s a lido just around the corner? I could climb on to the back of the very same creature and go for a nice cooling splash.

Jeff Koons is the answer. The Serpentine Gallery is putting on the first major British show by the American art superstar who, in a career that now spans almost a quarter of a century, has become famous the world over for turning completely banal objects into extremely fashionable pieces of art. His prices alone are enough to prickle your interest. A shiny balloon in the shape of a love-heart — the sort that you see bobbing about above a rampaging hen party — sold for well over $20 million a couple of summers ago.

Jeff Koons: Popeye Series isn’t a retrospective. Don’t expect a selection of iconic works. Rather, the New York-based impresario, who went from putting vacuum cleaners into Perspex display cases through casting balloon rabbits to creating a gigantic puppy out of flowers, now turns to a 1930s cartoon strip for inspiration in a series of which several of the pieces are on display for the first time.

Popeye is probably meant as a pun. It alludes to Koons’s eye for Pop. But with the spinach-eating sailor man as a starting point, it also conjures a life afloat. This series continues a long-held fascination with inflatable objects. They are about breath, Koons suggests, a symbol of optimism and our basic life force. Having explored basket balls and balloons, he now moves to plastic pool toys.

That is why all sorts of apparently intelligent people are likely to find themselves standing and gawping this summer at a blow-up plastic caterpillar that has got stuck in a step-ladder, a spotted-dog paddling pool turned into a log basket, a pair of rubber-ring turtles clambering up a chain-link fence. They will admire an inflatable lobster performing acrobatic feats. No wonder Popeye, who makes his appearance in the huge wall paintings, looks a bit bemused. If an athletic crustacean isn’t enough to bewilder, a pair of pornographic blondes with what definitely look like inflatable bosoms are guaranteed to make any self-respecting sailor squint. At least the lobster that hangs down between them has the decency to blush.

Koons’s aim, he says as he wanders around the show, putting the last touches to an immaculately produced exhibition, is to make art that doesn’t alienate anyone. He just responds to things, he tells me, things that he likes, things that won’t feel intimidating to people who aren’t familiar with art. He is not particularly to be trusted as an analyst of his own work. He doesn’t believe in criticism, he says. His art is all about acceptance. That’s all very nice, but in conversation he sounds rather like a cross between Jacques Derrida and Miss World: he finds some very convoluted ways of saying that he loves everything and wants us all to be happy. “We are perfect and our history is perfect,” he tells me. Or “I yam what I yam,” as the philosophical Popeye would have said.

I suspect that such innocence is an act, yet another layer in the endless montage of possible meanings that construct Koons’s work. On a basic level the “Liberace of fine art” (as Koons has been dubbed) speaks the language of kitsch. He says it with flowers or hearts or cute kiddies’ toys. But don’t fall for surface appearances: not least when what appear to be light plastic pool toys are actually cast in metal. You can’t tell without rapping your knuckles against them (which isn’t allowed). Every seam, every crease, every wrinkle of the plastic has been meticulously replicated; every bright colour or printed safety instruction flawlessly copied.

Koons may be making Pop Art’s simple satiric point: showing us the superficiality of consumer culture, how seductively its crass artificiality can be sold to us. But his works are conceptually more complicated than that. For a start he pulls off an impressive trick. He turns the “readymade” — one of the more complicated modern concepts — into a crowd-pleaser. Duchamp is given a Disney appeal.

His pictures are built up quite literally layer upon layer. His inscrutable sculptures (why is a paddling pool used as a log basket; what is a dolphin doing tethered to the Aga rack?) can be interpreted in much the same way. On a fundamental level they are all about sex. It is our primary response, suggests the artist who, during his brief but flamboyant marriage to an Italian porn star turned politician, produced huge close-up images of their marital rapprochements. Certainly, from the flirtatiously batted eyelids of a little blush-cheeked she-seal, through the belly-to-belly coupling of a plastic dolphin and a lobster to the fetishistic perfection of the painted faux-plastic surfaces, an air of eroticism slicks this entire show. Everything — even, perhaps rather controversially, a child’s pool toy — can be sexualised by Koons.

But beyond such sensual enticements are endless overlays of possible cultural references. Never has a lobster been so freighted with significance. It is Dalí’s telephone receiver; it is the moustache with which Duchamp defaced the Mona Lisa; it is a Fallopian tube; it is a phallus, it is a 17th-century still life. Koons drifts through the show commenting on a plethora of art-historical allusions. The mouthpieces on the underside of the blow-up dolphin apparently remind him of the teats of the wolf that nurtured Romulus and Remus. The purple-booted rows of caterpillar legs are like Duchamp’s descending nude or Balla’s Futurist dog.

Yet this is not an aesthetic that requires an academic to decode it. You can find your own reference points — often increasingly far-fetched. But it doesn’t matter where you go. What is important is that, by enticing you into taking notice of his work, Koons tempts you into the realm of further possibilities. Something that you might have overlooked as completely ordinary becomes suddenly — almost mysteriously — fraught with meaning.

It is elevated above mere kitsch. Art about kitsch too easily becomes a type of intellectual kitsch. But Koons takes a riskier tack. He presents himself not as the ironic outsider. His works are not mocking parodies. Instead, they try to show us a view from within. They speak of his feelings of almost childlike wonder. They pay awestruck homage to the objects they present.

Koons, in some way, is trying to show us something beyond the literal. It is not just a scrupulous copy that he fabricates. He improves on reality. He makes it ideal. That Flipper the dolphin is not just an extremely accurate replica of a pool toy; it is a pool toy finning its way towards the Platonic world of perfect forms.

The longer you ponder the objects that Koons places in front of you the more they take on a delirious, almost hallucinatory, feel. Do you remember the pure joy that you found as a child in the swimming pool? Can you relish the sheer brightness of those splashy colours? And then you blink and it’s gone. The bubble has popped. And — a bit like his paintings — the three-dimensional suddenly turns flat. You are standing there staring at a plastic crustacean. Surely it’s all a con?

But when you give up on the gallery and go down to the lido, remember that the cynic is really a disappointed Romantic. Koons gives you a lot to think about as you lie on your deckchair.

Jeff Koons: Popeye Series, Serpentine Gallery, W2, from tomorrow, until Sept 13.

www.serpentinegallery.org

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