"David Bowie is": the title is an unfinished sentence, which gives the verb a subject but no object, and it suggests that Bowie is everything and perhaps nothing, a whirligig of dressed-up personae, not a person. To begin with, he isn't even David Bowie. He was born David Jones, then renamed by a bossy manager. But is he Bowie, like the knife, or should his adopted surname be pronounced Boughie, like the branch? Or is any earthly appellation just an alias for a man – if he is one, since he always enjoyed flaunting his androgyny – who once announced: "I am a cyborg"?
On a grey arch through which you pass into the V&A's multimedia circus, Bowie himself makes a grand statement that introduces the proceedings. "All art is unstable," he says. "There is no authoritative voice. There are only multiple readings." By talking this kind of talk, he could have earned himself a PhD in semiotics during the 1980s: he is paraphrasing a modernist truism, first uttered by the poet Rimbaud when he said: "I is another" and repeated by Roland Barthes when he announced the death of the author and of authority, which set critics free to impute whatever meaning they fancied to works of art.
The quotation is our solemn initiation: this is a show that transforms the human being into a mutant, the pop star into a poet, the pin-up into a culture vulture who prepared for his career, according to an early Decca press release, by "reading through The Oxford Companion of [sic] Music, memorising much of it". Above you, at one point in the exhibition's dim labyrinth, hovers an aerial library, with suspended books that open like butterflies with flapping wings: a small selection of the intellectual influences that flutter inside Bowie's eclectic head.
The design, riotously cluttered and pleasantly bewildering, lives up to Bowie's promise of instability. We're conducted through a series of rooms or booths or wide-open arenas that evoke the worlds he constructed around him in the course of his journey from Brixton, where he was born, to druggy Soho, where he hung out during his days in an ad agency, or from grim, walled Berlin in the 1980s to red-carpeted and gold-plated Manhattan, his current home. A drab suburban bedroom, his earliest studio, suddenly reels and rocks as projections crawl along the walls. Then we float into a black cavity that is the outer space where Bowie stranded the hapless astronaut Major Tom. A glistening Top of the Pops stage is a habitat for Ziggy Stardust, after which we reach the dead end of a hut protected by barbed wire that conjures up Bowie's Berlin.
A Broadway dressing room recalls his performance in Bernard Pomerance's play about the elephant man John Merrick: a masterpiece of self-transformation, achieved without prostheses or makeup – Bowie relied on a crooked gait and a nervous, apologetic glottal impediment to create a character who seemed less a medical freak than a wistful lost boy, puzzled by his exclusion from the human race. Behind this is a screening room in which film clips take us through an anthology of Bowie's humanoids. In Nicolas Roeg's The Man Who Fell to Earth, the red-maned alien crash-lands in the New Mexico desert and confirms his extraterrestrial origins by telling a local woman: "I'm British." In Christopher Nolan's The Prestige he plays the scientific magus Nikola Tesla, strolling through a blitz of crackling static electricity and switching on a lightbulb by clasping it with his hand. In Nagisa Oshima's Merry Christmas Mr Lawrence he acts out a martyrdom that is also a masochist's consummation, like St Sebastian in military fatigues.
Oddly enough, there's one impersonation that doesn't convince. In a silver, skew-whiff fright wig, Bowie plays Andy Warhol in Julian Schnabel's Basquiat. Bowie knew Warhol, and is himself, as Christopher Frayling has said, "a singing Warhol", possessing the same range of talents – but he's somehow unable to catch the nerdy awkwardness of the man or mimic his droning voice. It may be that Bowie is just too graceful and sylph-like to wriggle into Warhol's sagging, acne-pocked skin. He is better, after all, at portraying gods or monsters than at being merely mortal.
Near the end, the exhibition becomes a little ghoulish. Clothes – Kansai Yamamoto's geometrical bodysuits, Alexander McQueen's violently distressed union flag frockcoat, some filmy pierrot drag and a ghastly pair of platform-heeled turquoise boots – were always the means of Bowie's self-revision: they made the man, successively remade him, and have outlived the capering faun who once wore them. Now they are modelled by a succession of white, blank-faced dummies that look like statues in a Greek temple, while Ziggy Stardust is laid to rest in a glazed coffin, the best-dressed cadaver in the mausoleum. It's good to know that Bowie, embarrassed by all this retro finery, confesses to being "faddy" and disparages his gladrags as a "hodgepodge".
Leaving these shed skins behind him, he has escaped into invisibility. As a boy in the London suburbs he was easily overlooked, merging with the crowd despite his eerie, mismatched eyes; now, living high above the streets somewhere in New York, he is ageing at a vertical distance from the gazes of the curious. The latest glimpse of him in the exhibition is at a fundraising event at the Metropolitan Museum in 2008, where, uniformed in a tuxedo, he serves as a deferential walker for his wife Iman: he glances away from the camera, while she flaunts for its benefit with a hand on her hip. But a dandified portrait by Snowdon, dating from 1995, suggests that he may have reincarnated himself, while sending a lookalike to the museum as Iman's escort. Preening in profile, Bowie here is David Beckham's identical twin. I'd need to see the tattoos to be sure, but I suspect that Becks might be harbouring a secret self, and that his entire career, on and off the football field, could be just another of Bowie's joking metamorphoses.
What's happening at the V&A is, quite literally, a canonisation. The mime Lindsay Kemp said that meeting Bowie was like having a vision of the archangel Gabriel, and the contributors to the exhibition catalogue are not much less worshipful. Geoffrey Marsh praises his "Universalist spirit", and Philip Hoare says that the "nearest cultural figure" to him is the poet-painter-prophet William Blake. To me, that sounds a bit inflationary, like the Bowie bonds issued in New York in the 1990s as an investment in future royalties that may or may not have eventuated. It's clear, however, that Albion achingly misses its once and future king. The catalogue begins by lamenting Bowie's abandonment of England in 1974 and ends by wondering why he doesn't come back. While we await the Second Coming, a map directs us on a pilgrimage to places in Soho where he once materialised. Marsh, in a spasm of infatuated mysticism, even asks whether Ziggy stays asleep in Avalon, like Tennyson's King Arthur, or can we will him to return "to overthrow the London of global capitalism"? So now we know who Bowie is – either King Arthur or David Beckham, depending on your taste or the urgency of your spiritual need. We get the god, like the government, that we deserve.
