Cat Power, whose real name is Chan Marshall, meets me in the lobby of her London hotel, and things do not go as expected. First, she is warm and inviting, when her smoky, melancholy records had led me to expect someone much more remote. And second, she is immediately in full swing with her impersonation of my English accent. “Life in the old dog yet, eh!” she says, after we decide to go to her room to avoid the noise and the smoking rules. “Good old Blighty!” she adds, as we get into the lift. I didn’t see this coming – not from a woman who grew up in the Deep South of the US, where she learned to sing about drunks and devils and depravity while dodging them, and has been dodging them ever since. I didn’t know she’d be funny.

“Aaaaand relax,” the 46-year-old says, sitting down on the rooftop balcony of her hotel room, after opening a bottle of red wine from the minibar and lighting cigarettes for us that she keeps in a leather pouch she bought in Mexico. As we talk, she tops up my glass but not her own, “I can get you drunk, but not me,” she says, because she has to go on stage tonight. If you’re a fan of Cat Power’s music, you might be thinking: “Well, hang on a minute, she was drunk the last time I saw her live, in fact she turned her back on the audience, muttered something inaudible, stopped in the middle of three songs and then walked off.” Such erraticism is indeed something her live shows became known for; in her own life there were psychotic breakdowns, and she went to rehab for alcohol and prescription-drug addiction.

Her diehard fans never wavered, though. For them, to know Cat Power’s heartbreaking, raw music is to love her unconditionally, giving her a rightfully elevated position in the American alt-rock scene, alongside contemporaries such as Sonic Youth and Will Oldham. Her blues singing and otherworldly coolness have also been noted by the fashion industry, with Karl Lagerfeld asking her to model Chanel jewellery after seeing her smoking a cigarette outside the Mercer Hotel in New York.

Currently, she is on a wave of rebirth, having changed record label, surprised her fans by becoming a mother, and realised her mind was never what others thought it was. Her new album is called Wanderer, she produced it herself, and it has already attracted excitement with its first single, Woman, a duet recorded with Lana Del Rey. One music website explained that the astonishment at their pairing was because Del Rey gets called out for being too fake, while Marshall gets questioned for being too real. But we’re not here to focus on the things that women are criticised for – this is Cat Power’s female solidarity album. She even has a Rihanna cover version on it, which came about after she heard it in a car – and hated it.

Facebook Twitter Pinterest At the tip of her fingers: blouse by Chloé at harrods.com; ring by thegreatfroglondon.com; belt by elliotrhodes.com. Photograph: Dean Chalkley/The Observer

She explains: a few years ago she was collected from an airport by the man who was then her lover, and the song Stay, a ballad, came on the radio. He said fondly: “There’s my girl,” as she got into the car, and her spirits soared – until she realised he was talking about Rihanna. “I turned off the radio. It was just terrible. So I’ll never forget that song, right?” Yet, years later, she was in a car, again, and heard it from start to finish, “and I then realised why Rihanna is so loved – because of her piercing direction, her vibrating, easy vocal, her delivery. I was on my way to the dentist or somewhere and, fuck, I was bawling in a taxi.”

It’s not wisdom that grips you when you are a mom, it’s awareness

One night she went to a karaoke bar – something she adores, private booths only – “and I found the song, Stay, and I sang it and sang it – then I said to my friend, ‘Do you mind if I sing it again?’ He didn’t care, he just wanted to get drunk and eat food. So I sang it 16 times.” When she started recording her album, she found herself singing it again. Her finished version starts with the chorus and then proceeds to disassemble its tight four-four rhythm into something else entirely. This album contains a lot of layered vocals, where she records herself singing the same line again and again, creating her own echo. I ask her how she knows when a song is finished, but she says it’s quite clear to her.

“Like when you’re cooking at your house, you know when you’re done. The purpose is served.”

Marshall grew up in a chaotic, poor family with a largely absent blues musician father and a mother from whom she would later become estranged. She has written about alcoholism, violence and assault and, on one song – Black – she sings of running all the way upstairs, to escape someone who “threw me in the bath with an ice and a slap / can of Coke down my throat / on his whole hands and knees”.

In her late teens, Marshall got involved in the rock band scene in 1990s Atlanta, a community that she says was full of loss, with people dying of Aids or heroin overdoses before their talent had seen the light of day. (Marshall’s grandmother later told her she was so proud of her not becoming a drug addict or a prostitute.) She had sung in church but had no formal music education, and at about 19 she taught herself the guitar, “just making rhythms, but my best friend Shaun, who passed away, showed me where to put my finger on one chord. That minor sound – sad – is the representation of most of my songs.” On the piano, meanwhile, her trick was to miss out the white keys. “But then I had a lover in South Africa who played saxophone and piano in his jazz club, and one night after the show he showed me exactly where to put my fingers to make a triad.” In her 20s she moved to New York and found a studio where she could record albums; Wanderer is her 10th.

Facebook Twitter Pinterest ‘That minor sound – sad – is the representation of most of my songs’: dress by Kitri at selfridges.com; belt by elliotrhodes.com; boots by Saint Laurent by Anthony Vaccarello at ysl.com; and tights by heist-studios.com. Photograph: Dean Chalkley/The Observer

Talking to Chan Marshall, it is always clear to me what she means. Yet when I come to transcribe the tape recording, it is hard to write up some of the sentences that stop and start, the missing words. You’ll have to imagine the repetitive clicking that takes over her tongue, deep in rhythm, when she says that her grandmother was a farmer, or the swooping gesture her arm makes when describing a sacred musical space, or the direction in which she turns herself, eyes shut, when her mind is looking for a thought that has escaped her. You don’t make records like hers by inhabiting your body like everybody else does.

Take the song In Your Face, with its slowed-down Cuban ballroom syncopation and lyrics about a man who protects his conscience with a military fanfare and by forbidding himself to think. Might this, paradoxically, be the first truly beautiful song about Donald Trump?

Those songs had been me trying to prove to myself that I was OK

She smiles and explains the title. “In Buddhism, your karma sits on your face. So, there may never be a justification publicly for that bastard – but perhaps one morning he’ll look in the mirror and realise he’s condemned.” She lets out a heartfelt “uuuuggh”, before saying these people come from cultures of hierarchy so there’s never just one of them maintaining the oppression. “It’s a pattern of power. But I think industrialised countries, the people, are becoming more infuriated. Rather than expecting a superhero, you know, a Churchill or a JFK to swoop in, I think people are actually becoming more and more open to paying attention to opposing positions.”

So you have some hope? “Well, you have to have hope; if you don’t then hopelessness leads to destruction. Or self-destruction. Implosion. Sorry. Sorry!”

Marshall ends so many of her thoughts with “Sorry, sorry!” that finally I ask her to promise to stop apologising for herself. “You don’t know how many times I have promised that,” she whispers, with a bittersweet twinkle in her eye, just about managing not to say sorry again. But it is clear that creating peace of mind for herself is something she takes more seriously now. Her old record label, Matador, wanted her last album, Sun, “to be a hit record, and the pressure was overwhelming”. So she moved to Domino, where she felt she could have “some kind of sacred, secret space with this record. I didn’t want to think about what anybody else wanted. I only wanted to think about what arrived in my brain.”

Facebook Twitter Pinterest ‘It would be amazing to fall in love again. That’s what everyone’s waiting for’: blouse and jacket by rokit.co.uk, and jeans by mih-jeans.com. Photograph: Dean Chalkley/The Observer

Something else that reinforced her, this year, was playing the 20th-anniversary concert of her album Moon Pix in the Sydney Opera House in May. It’s an album that she wrote, inspired by a nightmare when living alone in a farmhouse, and recorded in Australia in 1998, which was then described by Rolling Stone as her “breakthrough record”. The concert cemented something in her head about her own sanity; her own power. Marshall met so many fans who wanted to tell her what certain songs helped them through: a brother’s suicide, madness, loss. The more stories she heard, the more she realised what her small act of creation had achieved. Plus, she found a power in the songs themselves that didn’t fit with her memory of the girl who had written them decades earlier. “I didn’t know I loved myself then, when I was younger. But when we played them, I realised the great love that I had had for myself. Those songs had been me trying to prove to myself, you know, it’s OK, you’re all right – but now I know that she did know that, she did know she was worth love.”

Cat Power on Moon Pix: 'I'm alive today because of those songs' Read more

During that show, Marshall also said to the audience: “I don’t know how many of you here were back with me when I was mad.” I ask her about that now.

“You know, I felt like if I was… fucking wacko, then all these motherfuckers were wacko, too. And that’s the whole point, that we weren’t wacko. I definitely wasn’t crazy. And that’s one of the most calming things, the older that I’ve gotten – when I was younger, I wasn’t always able to find inner solidarity, but as I got older it was liberating. It doesn’t even matter if you’re an artist or not: the easiest way out of listening to the truth from a woman speaking it, is to tell her that she’s fucking crazy.”

It’s like Sinéad O’Connor, who wanted to tell the world that Catholic priests were sexually abusing children. People wrote her off – but she was right.

“I am so glad you brought up her name. No one brings up her name.” She pauses. “There were three records on rotation in front of my record player when I was 18, in my second apartment. This Girl’s in Love With You [Aretha Franklin], Blue [Joni Mitchell] and The Lion and the Cobra [Sinéad O’Connor].”

Three years ago Marshall had a son with a man she doesn’t name, whom she dated for months rather than years. (He is involved, and recently took their son for 10 days on his own, which she admits she found “nerve-wracking”.)

Facebook Twitter Pinterest ‘There’s so much happiness in the morning with us’: satin top by Ann Demeulemeester ( net-a-porter.com); trousers by dorothyperkins.com; boots Saint Laurent by Anthony Vaccarello by ysl.com; and necklace by viviennewestwood.com. Photograph: Dean Chalkley/The Observer

“When I was pregnant there was a lot of fear… would I survive birth? When I was born my mom left me at the hospital. She wasn’t well. I think I was very afraid of feeling disconnection from the baby. So any time I’d have that fear I would think back to my great grandma who was a sharecropper, I’d think about what she had to maintain with dignity. Just unapologetic, incredible hard work that still exists on the planet today. And that’s what gave me strength. But it’s not wisdom that grips you when you become a mom – it’s awareness, a new awareness that suddenly just grips your life. It’s a new kind of fear.”

As a fellow single mother of a sole child, I ask if she feels a pang when she sees nuclear families with two parents and a couple of kids. She says not as a mother, no, but as a kid she did. They moved house so frequently that she became curious about how other people’s families worked. “I was always the new kid, so I would go into new neighbourhoods to make a friend and I could see how nice it was, their lives: ‘Oh you guys make pancakes?’ And that’s how I live now, because I learned by watching all these humans. I ask my son what he wants for breakfast and I cook it for him. There’s so much happiness in the morning with us.”

Might you fall in love again?

“I’ll always be a romantic, I think most human beings have that part of their personality. But…” She groans, she smiles, she shuts her eyes. “It would be amazing to fall in love. That’s what everyone’s waiting for,” she says, finally. And she does not apologise.

Cat Power’s new album Wanderer is released on 5 October on Domino Records

Fashion editor Jo Jones; make-up by Jo Frost at CLM using Dior Backstage Collection and Capture Youth Skincare; hair by Paul Donovan at CLM Hair using VO5; photographer’s assistant Sam Reeves; fashion assistant Penny Chan

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