During a five-year break from music, Lily Allen got married, had two kids, and announced she'd had enough and wasn't coming back. Pop culture mourned; we had lost one of our greatest proponents of feminism, a symbol of originality, an icon of utter awesome-ness. But then, as she's wont to do, Lily changed her mind. Maybe she did quite fancy being a pop star after all. So she dropped the single Hard Out Here, creating a right old stir and a storm of controversy that she weathered in true Lily style; obstinately, loudly, unapologetically. Love her or loathe her, Allen is absolutely unashamedly herself - but she's also not too stubborn to admit she's changed her mind, or, perhaps, actually she could have said or done things a bit differently. While Hard Out Here was initially praised for challenging gender-role clichés and calling out a misogynist music industry, the video was also attacked for being racist -black female dancers were cast to twerk in the background. "Nothing I said was wrong, but I probably could have said it more articulately," she admits today. "I don't regret the video. Obviously I regret the fall-out from it. I'm not a politician - I just write pop songs. What I think is sad is that pop music is getting more and more vague. If you're a young girl who's writing pop music, you'd look at Hard Out Here and think, 'You know what? I'm not going to write about something that I think matters, because people are going to tear me to shreds.' That's sad. I don't want my music to be bland shit." Like her contemporaries Amy and Adele, Lily is fierce and unafraid, but she's not infallible.

She's also tight on time, so when the i-D shoot is over in East London, Lily suggests we do the interview in the back of her car whilst she does a mad dash across town for a secret appointment in Knightsbridge. As our plush taxi pulls out into the street, she coos at a couple snogging on the street and starts to open up as we talk about her career, private life and tendency to cause a stir.

Her comeback, after such an extended period away, was unexpected. People assumed she'd moved to the countryside, become a mum and lost her cool. But today, with her bleached blonde hair and Vuitton menswear rucksack (a gift from friend Kim Jones) she's far from the stereotype of mum at the schoolgates. "My days weren't as full as I wanted," says Lily of her return to music. "I stopped in the first place because I had kids, but also, I wasn't really in a great place towards the end of my last record. I was all over the shop and I didn't really know what I wanted in life. There were lots of coming-of-age questions and I didn't really want to be doing that in the limelight."

Though Lily was one of the first of a generation of stars to rise out of the new social networks of the internet - her success via MySpace was mutually beneficial to them both - she'd become disillusioned with its effect on the industry; people stealing music sent record companies into a spiralling panic. Sales plummeted, piracy rose and labels became increasingly desperate to wring as much out of an artist as possible. "There was no solution about how it was going to work in the future. I put a lot of work into what I do creatively, so it's a big thing, putting it out into the world knowing people can just take it," she says.

Lily spent most of 2014 touring her third album, Sheezus, often with her kids in tow. "When I wasn't with them it was really hard, and when they were with me it was amazing," she says. She did the UK festivals, supported Miley Cyrus in the US and headlined her own tour. "We had such a laugh on the Miley Cyrus tour," she recalls. "Miley's crowd didn't have a fucking clue who I was, which was the best learning experience that I could have had, because it taught me a lot about how to get an audience onside. I'm suddenly taking my profession more seriously than I ever have done."

Despite having shunned stardom for half a decade, her profile hasn't waned; she was never too far from the Sidebar of Shame or the pages of Heat! And the fashion world has never stopped loving her either: she remains one of Karl Lagerfeld's Chanel Ambassadors. "I don't quite understand why," she laughs, clearly bemused, "but I'm not going to ask too many questions!" Their relationship was an authentic one; when Lagerfeld saw the-then fledgling singer papped wearing his Chanel bags, he assumed his PR team were gifting her. When he found out she was a genuine fan who bought the bags with her own cash, he invited her to a show. They met properly when she got lost at a party at 31 Rue de Cambon, Coco's old apartment. "I had been DJing for them," she explains, "and found myself in Karl's design studio on my own, quite drunk. We got chatting about the physics of this shoe he'd designed, which had these polo mint jade rings in the heel. The next day they asked me to do the campaign."

She can hardly have been the safest option when it came to picking a face for the luxe brand, but that's part of Allen's charm. Where most spokesmodels barely utter a peep for fear of losing a campaign, Allen has never bitten her tongue. "I get myself into a lot of trouble, but I don't care. I'm vocal and honest, and that's the same reason I seem to do quite well on social media, because most other people in my position are a bit sacred and earnest and play the game," she shrugs. "I use social media as a platform to express my feelings. Sometimes I feel so incensed by something that I want to share it, or I want to know that other people feel the same way. A bit of affirmation, or validation," she says.

It's this approach to public life that makes her so divisive, but that has also cemented her place not just in our musical landscape, but our cultural one too. She's one of the few pop personalities willing to put her opinions on the line, and without her, British music would be a far, far duller place.

First record you bought? Ultimate Kaos. Last gig you went to? Jamie T at Alexandra Palace. You're stranded on the moon and can have one artist beamed up, who and why? Kurt Cobain, so I could make love to him and listen to him sing. What's your karaoke song? R Kelly, The World's Greatest. What song would you like played at your funeral? The Cardigans, Lovefool. What are your three biggest influences? The commute, people watching, relationships. What do you stand for? Honesty, fearlessness, humour. Which track of your own best sums you up? The Fear. It's about being a hypocrite, that's what I am. What do you want to achieve in 2015? To be content.@lilyallen

Credits

Text Stuart Brumfitt

Photography Matteo Montanari

Styling Max Clark

Hair Kei Terada at Julian Watson Agency.

Make-up Jenny Coombs at Streeters using Chanel spring/summer 15 and Chanel Body Excellence.

Nail technician Adam Slee at Streeters using Chanel.

Photography assistance Nicholas Riley Bentham, Nicola De Cecchi.

Styling assistance Bojana Kozarevic, Kristofj Von Strass.

Hair assistance Takuya Uchiyama.

Make-up assistance Mona Leanne.

Production Joe Streeter at Streeters.

Lily wears all clothing Chanel