Kylie's jubilee: Queen of pop celebrates 25 years at the top with a jaw-dropping performance

In case you didn't know it, we are in K25. No, this is not a new version of Y2K. Rather, it's a glitter-sprinkled anniversary, as Kylie Minogue celebrates a quarter of a century in the music business. Yes, 25 years since the Australian-born princess of pop made her breezy debut with "The Loco-Motion", during which time, the Grammy-winning, OBE-awarded artist has released 11 studio albums and sold more than 65 million records. As such, Team Kylie has decreed this musical milestone deserves a year of re-releases and surprise shows.

So it seems rather strange that I'm meeting Kylie – one of the few celebrities we all feel we can call by their first name – for what probably was regarded by her "people" as a minor footnote in K25. Holy Motors is not her film. It's directed by the mercurial Leos Carax, whose most famous film, Les amants du Pont-Neuf, is now two decades old. The real star is Carax regular Denis Lavant, who plays the mysterious Monsieur Oscar, who glides about Paris in a white limo, adopting different guises – from beggar to bandleader – for a series of bizarre "appointments".

For Kylie, who plays Eva Grace – another of these limo-dwelling shape-shifters – it is a small, supporting role. But, when K25 comes to a close, it will be this audacious, out-there work that she'll be most remembered for. Certainly more than her recent single, the electro anthem "Timebomb", memorable only for its video, in which Kylie writhed around on a motorbike in denim shorts. Holy Motors seems destined to be one of the most talked-about films this year after critics were left open-mouthed when it made its bow at the recent Cannes Film Festival.

When we meet, it's the day after the premiere – for which Kylie graced the red carpet in a stunning gold-sequinned Dolce & Gabbana fishtail dress. Today, she is dressed more modestly: a black crochet top, navy-blue trousers and a pair of platform heels that help elevate her elfin 5ft frame. Now 44, she looks in rude health – a relief after her well-publicised battle with breast cancer a few years ago. Though her pale skin sports minimal make-up, not even covering the few lines that cluster around her green eyes, her face shows none of the trauma that such an illness can bring.

She is exactly as you hope: smiley, sunny, unfailingly down-to-earth. She might have lived in London for the past two decades, but she remains an unpretentious Aussie girl at heart. Take her honest reaction to Holy Motors: "There were definitely parts that were outrageously beautiful, sublime moments. But there were also moments where I'm as confused as the person next to me," she says. "I need to see it again to form my own opinion – I don't know if it's ever going to make sense to me, but it gets you thinking and it gets you stimulated. Then you burst out laughing at certain points."

In contrast to some of the more outlandish moments (Lavant dresses as a flower-chewing goblin in one scene), Kylie's sequence is sedate, seductive. Channelling Jean Seberg, her blonde locks cropped, she sings "Who Were We?", penned by the Divine Comedy's Neil Hannon, to Monsieur Oscar. A forlorn melody backed by the Berlin Music Ensemble, far removed from the up-tempo tracks that dominate her output, she was asked by Carax, unusually, to sing it live on the set, rather than pre-record and mime to playback. "That was just magic to me," she says.

We're sitting on a quiet patio of a discreet hotel, one that seems to reflect her own modesty. There is a swimming pool close by, where her personal assistant of 12 years, Leanne, is sunning herself. When she shot Holy Motors, Kylie stripped back her usual retinue. "It was hard to tell them, as I knew they'd be disappointed – like, 'It's so exciting, she's going to do a film in France.' And I said, 'I'm sorry but I can't bring you.'" Imagine Madonna or Lady Gaga saying that?

As she arrives for the interview on time, almost to the minute, the PR has already declared his task "easy" with a client as "professional" as she. Her manner relaxed, she stops to pose for photographs just as willingly as she sits through her press duties. "I'm pretty much a realist," she says. "I don't think I've ever been like a sports person, who says, 'That was my goal.' I tend to trundle along a bit more. And then in the moment, I'll make a lot of effort." For the most part, she likes to keep it simple, bringing along Leanne and sometimes her manager Terry Blamey. "I don't step out of the house with an entourage."

She even screws her nose up at that essential celebrity trapping, the stretch-limo. "I find them embarrassing! I'm like, 'Please don't send a limousine!' I love to have this glamorous life sometimes, and if I didn't have any of that, I would probably be dressing up a bit more each day or going out on the weekend and making a real effort. But I get to live out those fantasies on stage, in videos or photoshoots. But if I can go somewhere you can wear wellingtons – and just be a total and utter bush person – I need that."

It's a curious thought: the girl that slipped on those gold hotpants in the video for "Spinning Around", starting a global obsession with her rear, tramping through the Outback. But then image, and the ability to morph, is something at which Kylie is a past master, her career spinning her from pop to indie to dance. Factor in her on-off acting career – from the role that sprung her to fame as Charlene in Australian soap Neighbours to her film debut in The Delinquents – and what you begin to realise is that her longevity comes due to her incessant thirst for re-invention.

Citing the original multi-hyphenate Barbra Steisand as her inspiration, she puts it down simply to a need to perform, in whatever medium she can. "If you're a performer, at least in my understanding of being a performer, then you perform! If I couldn't perform, I would drive my friends nuts. It's been a long time since I haven't worked, but there was a time when I wasn't working a lot, and I remember my girlfriend saying to me, 'Can you go and do something?' We'd be at a flea market and I'd be like 'Da-da-da-da…' My Mum says that I was a toddler, in the crib, doing this kind of thing. It's part of me."

This much is true. As a youngster in Melbourne, she can remember bounding on stage for a talent contest, playing "Run Rabbit Run" on the piano. She won second prize. Though she was the eldest of three – her father Ronald was an accountant, her British mother Carol Ann a former ballet dancer – it was actually younger sister Dannii who was famous before she was. Dannii had a slot on Aussie children's talent show Young Talent Time, which Kylie appeared on only once (and had to plead not to be called "Dannii's older sister"). But when she auditioned alongside Dannii for a role in Australian soap The Sullivans, she beat her sister to the part.

Leaving Dannii in the dust (arguably for the rest of their careers), she moved on to Neighbours in 1986 and widespread fame. The UK broadcast of Charlene's wedding to Scott (played by her then-boyfriend Jason Donovan) drew in 21.16 million viewers, putting it in the top 30 most-watched TV events ever over here. But then soap star was never the limit of her ambitions. By 1990, following a string of pop bubblegum hits including "I Should Be So Lucky", she had quit the show, dumped Donovan and started dating INXS front-man Michael Hutchence, who famously said his favourite hobby was "corrupting Kylie".

When she turned up to the 1989 premiere of The Delinquents with Hutchence on her arm, she was wearing a bleached-blonde cropped wig and thigh-flashing dress. In the past, she's called him "Byronesque", noting how the late singer opened her up to art and literature. "The best way I can describe how my life changed with Michael is that up to that point it was like I had worn blinkers and the blinkers were suddenly taken off. It was a combination of him, of my age, my willingness and my desire to learn about the world."

You only have to look at the image makeover she undertook for her 1990 album Rhythm of Love to see the effect two years dating Hutchence had on her; Bardot-like hair, fishnet tights and heavy mascara replaced her trademark perm and bauble earrings. But even if the sex-kitten act came easy, exploring other facets proved more challenging. "So much of what I do and what I've been focusing on in music is putting different things on and being shiny and 180-degree focused," she says. "But no one's shiny and happy all the time."

She recalls another unexpected decision – her duet with Nick Cave, the 1995 murder ballad "Where the Wild Roses Grow". "I don't know if you remember at the time, but that was a… well, not scandalous but a bit of a shock, a surprise. It was like, 'You're singing a murder ballad? He's killed you? You're floating in a lake!' Of course I'm intrigued by that. It's exciting for me." Ironically, this song is the only thing Holy Motors' Leos Carax (who was introduced to the singer through a mutual friend, fellow French director Claire Denis) claims to have known about Kylie.

As her romance with Hutchence, her work with Cave and now her role in Holy Motors show, deconstructing her pop persona has become essential for Kylie, not just for prolonging her longevity, but also maintaining her sanity. "I think it's been a big challenge for me to be seen not as 'Kylie' – in inverted commas – because that's who I've become. It's actually hard for me, but I think it's harder for the audience, which means I've got to work twice as hard to be believable."

She admits that Holy Motors has allowed her to explore "other sides to me" – literally and thematically. That Monsieur Oscar goes from one character to the next, showing "how we present ourselves in the world in different moments" must have appealed to her. It certainly marks her most significant film contribution to date. Mirroring the post-Cave slump her career took with 1997's Impossible Princess album, her screen roles in the 1990s – opposite Jean-Claude Van Damme in video-game adaptation Street Fighter, playing in lame slacker comedy Bio-Dome – were ill-advised at best.

That she mounted the mother of all comebacks in 2000, showing just how aware she was of the need to reinvent. From performing at the closing ceremony of the Sydney Olympics to releasing the album Light Years – with "Spinning Around" as its centrepiece – such was the clamour around her, it was little surprise that she dubbed her next album Fever. With that 2001 album featuring what would become her signature tune, "Can't Get You Out of My Head", it was as if the green fairy she played for Baz Luhrmann in his fantasy musical Moulin Rouge! that year had granted her every wish.

Of course, life does have a way of undercutting fantasy. It was in the midst of her 2005 Showgirl tour that she was forced to cancel the remaining dates, when she was diagnosed with early-stage breast cancer. "Possibly because I was diagnosed mid-tour, it was my goal to get back and perform," she reflects. "You hear stories about people suffering from a major illness or having a trauma in their life that makes them question what they do: stressed-out bankers go, 'This isn't for me, I'm going to take up watercolour!' But I just realised that, no, this is what I do, and I want to do it better than I did before."

In the wake of her 16-month recovery, the exposure her illness was given led to an influx of women getting screened – something doctors dubbed "The Kylie Effect". "Obviously it's a badge you don't want," she says. "No one would choose to wear that badge. But that's what happened in my life. And I'm by no means being pompous, but girls have written to me or come up into the street and they've said, 'I was diagnosed because of you.' And it's a hard thing to even comment on, because it's such an awful, awful thing, but there's something positive in among that."

While her then-boyfriend, the French actor Olivier Martinez, stood by her through the worst of the treatment, their relationship did not last. For the past three years, she has been with a younger beau, the 34-year-old Spanish male model Andres Velencoso, who she met when he starred in an ad for her male fragrance Inverse. She's called it her most fulfilling relationship to date. "I'm up and down, he's much more consistent," she says. If anything, her illness taught her to find equilibrium in her personal life: "There's more balance than there used to be."

Not that she's slowed down. With her business empire expanding (perfume, lingerie, even a children's book, The Showgirl Princess), I wonder whether she still gets a buzz from touring. "Absolutely," she nods, though it's not, as you might think, for the adulation or adrenaline. "You get to opt out of life a little bit because you're living in the tour bubble. And then sometimes when real life becomes difficult, we'll joke, 'Let's go on tour again!' You know what you're doing, someone puts a call sheet under you, you're on this plane, that bus, you're performing here, here and here. In a way, it simplifies life."

To the consternation of her myriad fans, Kylie was recently prevented from making what would have been an emotional reunion with Jason Donovan at London's Hyde Park, as part of the Hit Factory show. At the concert organised by Pete Waterman, the producer who effectively launched her singing career, Kylie and Jason were due to perform their duet "Especially For You" for the first time in 23 years. But fans were left hugely disappointed when the gig was cancelled after incessant rain turned the park into a mud-bath.

There is still talk that the show will be resurrected at Christmas at London's O2 (shortly before Kylie takes on the role of artistic ambassador for Sydney's New Year's Eve fireworks). For the moment, however, she's looking to a more imminent gig. Headlining Proms in the Park, she will be joined be a 53-piece orchestra "doing different interpretations of my hits". Again, it comes as part of the K25 celebrations; beginning with the release of an acoustic version of "On a Night Like This" earlier this year, a whole album of orchestral and acoustic versions of her songs is planned.

If this is yet another move to keep us guessing, she doesn't overanalyse her strategy. "I think you need to have good songs. Good songs, and present them well, and stay connected with your audience." Like many celebrities, she is frequently on Twitter doing just that. "I don't know how long that's going to last. Maybe they will end up going, 'We're sick of this. Twitter's not satisfying us any more.'" But even in this digital age, she knows how to truly reach out to her fans: "You have to go on the road, and have that animal, raw connection." And that, she's never lost.

Kylie Minogue headlines Proms in the Park, to be held in London's Hyde Park, on 8 September. 'Holy Motors' (18) opens on 28 September