Wow. Just saying it could even make it happen.

In April 1979, 20-year-old Kate Bush undertook six weeks of her first tour, The Tour Of Life, since when she has not performed one concert. Reviews at the time remarked upon "her unabashed obsession with sex" or noted "you're distracted by Katy being wheeled around in a giant satin-lined chocolate box". Others hailed "a dazzling testimony to a remarkable talent" and "the best welding of rock and theatrical presentation that we're ever likely to see." Despite such critical confusion, it was a triumph. "It was lovely", said Kate. "And the greatest encouragement I could have possibly had." The shows have since entered rock-lore. Kate was aiming for "something special", incorporating dancers, props, magic and seventeen costume changes. As she'd frequently be lifted and carried by these dancers, she needed a microphone she didn't have to hold. "So my sound guy basically invented the radio mics you see nowadays," she's said. "He made it out of an old coat hanger, which he bent into shape."

The young singer's experience was marred, however, by the death of the tour's lighting technician, Bill Duffield, in a tragic accident. Also, Kate didn't enjoy the over-emphasis – from others - on her sexuality, and disliked the requisite promotional activities. Taking control of her business affairs with her family, she became a (very successful) studio animal, happily finding that the more she retreated into unavailability and mystique, the more her legend grew.

And so, as they do, thirty five years went by. Albums, accolades and honours occurred with charismatic irregularity. After Hounds Of Love was universally recognised as a masterpiece (we tend to forget that it rebooted a wobbling career), her best albums – The Sensual World, The Red Shoes – were unfairly underpraised. There were twelve years – wherein she focused largely on motherhood – between The Red Shoes and Aerial. Then, with – by her standards – indecent haste, there followed The Director's Cut (a misguided re-hash of earlier songs) and 50 Words For Snow. The world had missed her so much that these last two, her weakest, were overpraised.

Although she had murmured three years ago that she might play live again before she became "too ancient", nobody really expected today's announcement that she'll play fifteen nights at Hammersmith Apollo this autumn. It's one thing for Prince to announce he's playing your local at five minutes' notice, but he is not known as a shy retiring recluse to the extent that Bush is. One hopes that people realise that she is no longer twenty, and is as unlikely to present a limb-shaking, gyrating, visual extravaganza, acting out each song's storyline, as Bowie is to dust off his Ziggy wardrobe or her good friend Peter Gabriel is to sport a giant sunflower on his head. It may be wise to expect a more sedate, mature, singer-and-piano affair than the video films we saw. (For kicks inside your house, check out – as well as her grand run of epic videos - her 1979 BBC TV special. Her performance of 'The Wedding List' is an extraordinary, operatic marriage of mania and control).

And yet, something good is going to happen. Kate Bush has always operated outside logic and function. People who routinely claim to loathe "pretension" and "artiness" in music line up to hail Kate's genius. She's a British artist who defies the British tradition of mocking those who have lofty ideas. She is also nothing if not prog, though again many of her fans would shudder at the description. Discovered and mentored for EMI by Pink Floyd's David Gilmour, and a long-time Gabriel associate, her notion of the perimeters of the norm were very much influenced by dance lessons with Lindsay Kemp, by early Genesis and the musicians from Alan Parsons Project and Cockney Rebel with whom she recorded her first demos. She has the happy knack of disregarding trends, of overriding cool: who else could rope in guests ranging from Elton John and Eric Clapton to Rolf Harris and Stephen Fry, yet still be a press darling?

She has always known what she wanted. When the head of EMI told her that her first single would be 'James And The Cold Gun', her strategy in support of 'Wuthering Heights' was to burst into tears in his office. "I had no way of dealing with that", he has since said. "I caved." She emerged, contrarily – out of time, out of place, floating above the here and now - in the heyday of the punk era. A 19-year-old, singing songs she'd written aged much younger, referencing Emily Bronte and Gurdjieff. Later, Joyce. When young people are moved by books, they are really moved by books. It may seem absurd now but her artistic voice was startling in its candour then. On The Kick Inside she sang of lust and eroticism as perceived through the female gaze: only Joni Mitchell and one or two others had previously done this with unselfconscious commitment. You can argue specifics, cite Bessie Smith, but it certainly wasn't common in the pop music world. More sensually, she didn't just sing OF these urges and fevers, she expressed them, with no filter. The sound of her swoons and sighs was pansexual, unfettered, rhapsodic.

Lionheart, rush-recorded, may have lapsed at times into jazz-hands camp and peculiar patriotism, but few albums sound as much like afternoon sunlight nudging your window. Never For Ever saw swans, cats and whales swooping from beneath her skirt while referencing Henry James and Truffaut, gave us 'Army Dreamers' and 'Babooshka', and in 'Breathing' showed us how much deeper she was ready to go. She self-produced the experimental The Dreaming (Vietnam, Houdini, indigenous Australians) then built a studio in her barn, emerging with Hounds Of Love – the Eighties album that doesn't sound Eighties, yields her best-loved singles and still finds time for a full-on prog suite on Side Two. The Sensual World, delirious with finely-gauged abandon, spun on a sotto voce "yes" as tactile as anything Marvin Gaye or Al Green had conjured. And if The Red Shoes has, bewilderingly, been given bad press, it is a curious music-lover who doesn't spring about to 'Rubberband Girl' or cry their eyes out to 'Moments Of Pleasure' or 'Top Of The City'. These last two are so poised - as brittle as you can get without relinquishing your structure - that they seem to switch from ice to warm water to ice again. 'Moments Of Pleasure' is the only song ever recorded that I cannot listen to because it's too moving.

After a dozen years out, Kate Bush came back with a sea of honey and a sky of honey, much birdsong and, as a climax, 'Nocturn/Aerial', a chill-out/rave hybrid that shouldn't work on any level but does work and play on every one. She was welcomed, naturally, and the muddled Director's Cut and the rather literal-linear, sometimes colourless 50 Words For Snow performed solid myth-maintenance.

Her influence on subsequent singers and musicians is perhaps most evident in those who crave autonomy and move at their own pace, curl up in their own wilfully awkward aesthetic shapes. Little could be more reductive here than a glib list of female performers who owe her a debt (though it would be a lengthy one): it is happier and healthier to insist that her legacy pervades all artists, male or female, who ignore what is expected and demanded and plough their own furrows, furrow their own brows, concern themselves more with the timeless than the topical. Kate Bush is no genre but Kate Bush.

Back when eulogising Gurdjieff on 'Them Heavy People', she sang: "They opened doorways that I thought were shut for good." Not to get too heavy about this – after all, she sang about euphoria induced by washing-machines on Aerial – but the Before The Dawn concerts and the unlikely return to a stage of the eternally elusive Kate Bush promise to open a doorway to moments of pleasure which fuse memory, magic and a mystery solved yet – happily, always - unsolved.