Does she dance? She dances ON, and damn you for even asking.

After darkness falls at 7.45 sharp, the voice of Miranda Richardson, in character as the titular white witch of "Lily" from 1993's The Red Shoes, recites Vedic imprecations from the centuries-old Gayatri Mantra ("O thou who givest sustenance to the universe, from whom all things proceed, to whom all things return, unveil to us the face of the true spiritual sun hidden by a disc of golden light, that we may know the truth and do our whole duty as we journey to thy sacred feet...") and that song's almost hip hop beat thumps and bumps out into the auditorium, the living, breathing Kate Bush – and yes, this is only the first time that you pinch yourself in disbelief that you're actually seeing her as a flesh and blood human being, and it won't be the last – sashays in from the wings at the head of a casual quasi-conga formed by her backing singers.

A whole mountain of covertly misogynist bollocks has been written in the run-up to the Before The Dawn residency, with much snickering about whether at 56, and inevitably fuller of figure than her willowy 'Wuthering Heights' self, she would still be pulling those Lindsay Kemp-tutored interpretive dance moves. One dinosaur even wrote that to do so would be "unbecoming".

Barefoot, her shoes thrown in the lake some years ago along with any cares about what may be 'becoming', and so softly beautiful that everyone falls hopelessly in love with her in an instant, her face radiates pure joy around the room like a lighthouse beam as she gently pirouettes, her black velvet tassles flailing. Three minutes into the song, there's an Orbison growl and she intones, sotto voce, "this is my space". And her space it is. The night's barely begun, and already, she's owned it. Hammersmith, scene of her last full concert 35 years ago, is her domain again, for 22 nights which sold out, famously, in just fifteen minutes. And if there's ever been a warmer and louder burst of applause at a pop concert, I can't remember it. Her response, amid the clamour, is difficult to make out, but I swear at one point she jokingly asks us "Where have you been?"

Where, indeed. In BBC4's Kate Bush recent documentary, John Lydon perceptively stated that for a lot of his punk friends, Kate Bush was "too much". In two words, he summed up the case against Bush, or at least, the alibi for anyone who ever found her a little off-putting. As a child, she scared me, for reasons largely connected to her too-muchness. Her eyes, mouth, gestures and vocal range were all too big, like the granny-wolf in Little Red Riding Hood, and that, to children, is always going to be unsettling. I would, later, learn to love what had once filled me with fear. Re-immersing oneself in this woman's work is frightening in a different way: it's hard not to be daunted by so much sheer genius within one back-catalogue.

Perhaps it isn't surprising that Rotten's coterie found her unpalatable. Kate Bush, uniquely among the towering icons of the early 80s, didn't come out of punk, but from prog. Inspired by King Crimson and Pink Floyd as much as David Bowie, Stevie Nicks and Roxy Music, and mentored by Gilmour and Gabriel, the multi-chord complexity of her works and the unashamed theatricality of its presentation was rooted in 1973, not 1976. The Kentish soil from which she sprang wasn't that of the Bromley contingent, but that of Soft Machine, Caravan and the Canterbury set, and a century earlier, that of William Morris, whose Red House in Bexleyheath, a stone's throw from Bush's childhood home, was the rural retreat for Rossetti, Elizabeth Siddal and the Pre-Raphaelite set. That unfettered artsyness was the air she breathed, and is the reason Bush should be seen as the last and loudest gasp of the bohemian 1970s, an island of baroque excess amid the tapered strictures of the New Wave.

Her influence upon subsequent performers, particularly female ones, barely needs restating (make your own list), and the same goes for her questing, challenging, experimenting spirit and her commitment to stretching the boundaries of pop. In her early years, Bush was never fully given due credit by a male-dominated press, who scoffed at her as a deluded am-dram princess. Their hairy, hoary heroes were still mining the same old blues-rock seam while Bush was drawing on literary and philosophical influences from George Gurdjieff to James Joyce, imagining an unborn foetus' fear of nuclear apocalypse or empathising with the military mother's grief at her son's flag-draped body bag, and skipping between more musical styles in the space of an album – a single song, even – than most bands dare in their entire careers.

That legacy, arguably, would have been diminished somewhat if her comeback concert had been a cheesy cabaret retread of her greatest hits, a West End-style production of Kate Bush: The Musical. (Not that Before The Dawn isn't theatrical in spades, but more of that shortly.) It's a monumental relief, then, to see her returning resolutely on her own terms, putting on a show which, perhaps pointedly, features nothing from her 1979 setlist, drawing instead on just four albums: Hounds Of Love, The Red Shoes, Aerial and 50 Words For Snow, indicating a refusal to retread her juvenile footsteps and hinting that those are the records which, whether due to recentness of release date or thematic factors, she's particularly feeling at the moment.

Not that she doesn't throw a bone to the hit-hungry. The first act contains a couple of the Whole Story mega-tunes, one of them right at the top of the show. 'Hounds Of Love' ought to attack like a hundred-foot horse with hydrogen bombs for hooves. And it... doesn't, quite. (First night issues with the sound levels, perhaps, and easily tweaked.) But it does provide the first proof that Kate Bush has still got it. "Oh, here I go!", she belts out with Beaufort Scale lungs and, yes, there she goes. After 'Joanni' from Aerial, a tribute to Jeanne D'Arc which shows her inner Catholic schoolgirl (Kate was raised by doctors and nuns, poised between the rational and the irrational), we get 'Top Of The City' from The Red Shoes, and when she hits the big, spine-rattling note ("I DON'T KNOW IF YOU'LL LOVE ME FOR IT..."), any lingering doubts about the enduring power of her voice are vapourised.

That song barely has time to fade when a minor chord on the keyboard causes an intake of breath that seems to suck all the air from the room. 'Running Up That Hill' is one of the greatest songs ever written. The NME once deemed it the greatest of all. The dawning realisation that we're witnessing it performed live, note-perfect and in extended form, is overwhelming.

When that single came out, Bush was only 26, an age at which many of today's hipster darlings can still pose as upstarts, but THEN already seemed like the most demure, mature, dignified, elegant elder stateswoman of pop, exuding utter class among the TOTP trash. And yet, it's filth: a single in which a woman daydreams of striking an inverse-Faustian pact to experience sexual intercourse from the point of view of the male. (Other, more diplomatic interpretations are available, but frankly, any reading of 'Running Up That Hill' which doesn't accept that "Do you wanna know that it doesn't hurt me?" and "See how deep the bullet lies" are about cock is a non-starter.)

Few other artists would consider such a thing. But its parent album was even more extraordinary. Hounds Of Love functioned as Kate's rapprochement with mainstream pop, after the (superb) Aborigines-with-Fairlights weirdness of The Dreaming, and its first side was a hits-fest, but she still found space to fill the whole of side two with a conceptual art statement, The Ninth Wave - a half-hour suite consisting of the inner monologue of a woman who is floating adrift at sea, and imagines herself variously as a corpse trapped under the ice, a ghost in her family home, and a witch on the ducking stool. "They're completely alone at the mercy of their imagination," she once tellingly said of The Ninth Wave's fictional protagonist, "which I find a completely terrifying thing."

It's a piece of which she's clearly still proud, because she performs it in its entirety tonight. After 2005 comeback single 'King Of The Mountain', her percussionist, who looks like a crew member from the Black Pearl (fittingly enough, for the nautical theme of what follows), takes centre stage and literally whips up a storm. Footage of the eye of a hurricane gives way to an interlude in which an amateur stargazer attempts to report a mayday from a stricken boat. The screen falls, and the entire stage has been transformed into the undersea ribcage of a shipwreck (with heavy overtones of the Jonah & The Whale story).

The backing singers, notably including Kate's son Bertie (who, she has said, gave her the strength to make this comeback), now double as fellow victims of the capsized vessel. There are trap doors, scary skeletal fish-people, and an overhead rescue helicopter. There's a deliberately corny scene in which the lost woman's son and husband exchange good-natured banter about burning sausages and during which – turn away now if you don't want spoilers – Bush magically appears in a corner of the room. There's a stunning choral finale borrowed from Werner Herzog's Nosferatu. And the PA's surround sound comes into its own, with the recorded voices of Bush's own family – and Robbie Coltrane – attempting to shake her awake with a matronly "You must wake up, child" and a more affectionate "Wake up, luv." Suddenly, you understand why the show needed a dress rehearsal.

The predictions of hardcore Bush-spotters that the photo on her website of Bush wearing an orange lifejacket prove, then, to be bang on the money. As do the assumptions about the significance of the underwater flora on the gig ticket itself. After a 20 minute interlude, Act two of the show is taken up with another concept piece, this time the A Sky Of Honey disc from Aerial.

The title of that album, of course, is a triple entendre. Firstly, its subject matter is, literally, things that happen in the air. Secondly and thirdly, Bush is both an aerial and an Ariel, half lightning-rod tuning into the elements, half mythical sprite. It's crucial, in the understanding of Kate Bush, to realise that she isn't a total alien like Prince or Bowie. She's one of us, but more so. A heightened version of ourselves, a conductor of the sensual world (incidentally, it's a minor pity that nothing from The Sensual World itself gets played). An ultrahuman.

The bucolic reverie of A Sky Of Honey begins with an enchanted forest, 'real' snowfall, and an almost life-sized wooden artist's mannequin. It involves slow-motion footage of birds in flight, cloud formations developing and the moon rising. The singer-dancer-actors, this time, play skull-headed bird-people, while the Rolf Harris role in 'The Painter's Link' is taken by Bertie (which is probably for the best), who also performs a new song, 'Tawny Moon', inserted near the end of the suite. There are attendees who, after the show, will complain that this section is boring. But, while it admittedly lacks the drama and peril of The Ninth Wave, there's nothing that's boring about the ending: Bush, wearing a giant pair of crow's wings, spreads them wide like a gothic Pygar and – for just a few seconds – flies, as if in an affectionate fuck-you to Faith Brown's famous wire-flying "Wow" pisstake all those years ago.

It's an incredibly emotional evening, but there are no grand speeches from Bush, just a few words of heartfelt thanks for our "warm and positive" response (there have been standing ovations every few minutes, it seems, over the course of a nearly three-hour show), and a moment when, jarringly if correctly, she describes her band - seasoned session men and former members of Weather Report, Mezzoforte, Pink Floyd and Dire Straits - as "shit hot" (it feels wrong to hear Kate Bush swearing, somehow).

She encores by sitting at the piano for 'Among Angels', the closing ballad from 50 Words For Snow, then brings back the band for a marching-paced 'Cloudbusting'. The line "Ooh, I just know that something good is gonna happen" is redundant: It already has. Another standing ovation. "Does that mean you liked it?", she asks, coy as anything.

Understatement. From Kate Bush. Now there's a thing.