Gustav Klimt has become a cliché. No doubt it's the fault of the endless spin-offs. But surely even the most sceptical will feel a bit of a frisson at the news that a show of his work will be opening at Tate Liverpool this week.

This show, Gustav Klimt: Painting, Design and Modern Life in Vienna, is the first substantial exhibition of this most popularised of painters to come to this country. It's certainly a coup for the European Capital of Culture. Klimt, after all, counts as an artistic A-lister. He is the icon-maker of our modern age. You only have to stand in front of one of his masterworks to know why. It's not just the shimmering surface that entrances you: it's the slow, languid pull of a deeper temptation. You slip into the clutches of his opulent confections, like his famous lovers into their luxurious embrace.

No wonder the booking lines at Tate Liverpool are buzzing. But does this show offer more than mere sensual indulgence? Or are we just coming to lounge indolently on the cultural chaise longue?

If you are hoping for a glorious run-through of the golden greats you will be left underwhelmed. There may be a handful of his celebrated seductresses to snare your attentions: a delectable Nuda Veritas with her mother-of-pearl pallor; a darkly inveigling Judith with her curled tigress's claws and a rapturous duo of entwined water serpents. A scattering of haughty society beauties do turn up: the trophy wives of the patrons whom Klimt cuckolded even as they paid him to paint.

Even the artist himself might be present in the form of his splendid allegorical golden knight who, riding defiantly towards his fate, is often seen as a symbol of the creative spirit. But, of the 25 or so Klimt pictures that now go on display, the most familiar are missing. The Kiss that adorns a thousand bedroom posters, the dreaming Danaë of the myriad Valentine cards and the iconic Portrait of Adele Bloch-Bauer I, which acquired a cult status when it fetched a record-breaking $135 million at auction a couple of years ago, are all absent.

Many of Klimt's works are too precious, too fragile and too highly treasured by the museums in which they are kept to be allowed to travel. But, unfortunately, Tate Liverpool must also compete with another Klimt show that is running in the Neue Galerie in New York. Since Klimt not only worked notoriously slowly but much of what he did finish was famously destroyed in a fire, there are simply not enough of his pictures to go round.

So the curators of this show have decided to widen their outlook. They show us the Austrian Modernist in a broader context. Naturally Klimt takes top billing. You can trace a more-or-less chronological progress of his vision and style in a show that represents the range of his work, from the serene classicism of early portraits through graphic designs and architectural friezes to his “golden phase”, when, inspired by trips to Venice and by the Byzantine glint of the basilica in Ravenna, he created the mosaic-style compositions that turned the Viennese bourgeoisie into glittering beauties.

Here, you can find Klimt's sun-flecked landscape squares (their patterned surfaces are almost the precursors of abstraction); his daring erotic sketches, a highlight of the show; his one-off stone carving (a mere curiosity); the scarf that some say he designed (more probably one of the first of the many fashion spin-offs that he sparked); and the smock that he painted in. Anything that Klimt touched appears to be coveted: down to the aesthetically indifferent bits of foreign tat that he collected for his studio.

Yet in a show of something like 250 exhibits, only about a third of the pieces are by Klimt himself. We have grown accustomed to viewing this artist's oeuvre a bit like the mosaic fragments that he himself worked with. Dispersed about their various museums, they glint like the scattered elements of a wider vision. But this exhibition now sets out to slot them back into the background against which they were originally intended to be admired.

This broader context finds its roots in the British Arts and Crafts Movement, which, focusing on the importance of the actual process of making, struck a chord with the visionaries of turn-of-the-century Vienna. Here, painters, designers and architects were coming together in search of an ideal of harmonious integration. British artists such as Charles Rennie Mackintosh and James Herbert McNair showed in the exhibitions of the Viennese Secession: the groundbreaking Modernist movement which, founded in 1897 with Klimt as its president, broke with the stuffy traditions enshrined by the Austrian Academy. It was collaborations such as this that paved the way for the Wiener Werkstätte: the co-operative society of artists and craftsmen established (with the support of Klimt) in 1903 to counteract the shoddy craftsmanship of mass production.

But it was not just the individuality, beauty and precision of each object that Wiener Werkstätte artists were interested in. The patrons, too, were considered of crucial importance. It may feel embarrassingly sycophantic but, to put it bluntly, the community of those who created could not continue without the community of those who coughed up.

It is the patrons who provide the impetus to a show that progresses through a succession of re-creations of haute bourgeois interiors. Here, works by key players of the period (the architect-designer Josef Hoffmann probably most prominent among them) are reassembled from collections the world over - often for the first time since they were first disbanded. It feels a bit like visiting the V&A. There are showcases of cutlery and coffee sets, pieces of furniture and designs for light fittings and carpets.

The visitor soon gets the gist. Everything, however humble, matters, from the coal scuttle down to the loo-paper dispenser.

But I doubt whether Klimt, notoriously fussy about the installations of his exhibitions, would be particularly satisfied with these sketchy reconstructions. They evoke only the most fleeting sense of the rooms that must, in their day, have felt truly astonishing. Far better to peer into the sepia photographs and imagine. You can almost hear the click of the ghostly footsteps that cross the polished spaces that they capture. Modernism's geometries find their precursors in these stark designs.

More successful is the re-creation (using the same materials and techniques) of the 1902 Beethoven frieze. In this epic design, Klimt seeks to summon the spirit of the Ninth Symphony and present its grand struggle between hostile powers (here represented by a naked temptress and a hideous squatting ape) and the spirit of Joy which comes to its climax in an ecstatic kiss. This frieze, originally running high above craning heads, has been brought down to eye level. The spectator can almost step into the drama.

But then the breaking down of barriers is a great part of the point of this show. It was certainly the point of Klimt's vision. The exhibition makes this plain with a studious clarity. But nowhere is this erosion of boundaries more instinctively sensed than in Klimt's most populist pictures. Despite a plethora of carefully assembled objects, spectators should still take this opportunity to spend as much time as possible with Klimt's enraptured beauties (though a lowering work by his protégé Egon Schiele would also make a trip to this show worth it in its own right).

Let them seduce you. Theirs is a world in which fundamental opposites meet. Spiritual meanings may be discovered through the senses. The priestly and the pornographic merge. Divine beliefs, Klimt suggests, can be embodied by beauty. That's not a greetings-card cliché. It's a subversive force.

Gustav Klimt: Painting, Design & Modern Life in Vienna 1900 is at Tate Liverpool (0151 7027400), from Friday until Aug 31

Editor's choice

• Hitchcock's 50 most memorable moments
• Vote for musical perfection
• Proms Podcast with Matthew Barley