Milk pours out of FKA twigs's fingers, at the end of arms whose soft bulk suggests a kind of ant-strength. Spray-painted in gold and writhing beneath her with biomechanical need is a doppelganger, lapping at the cascading liquid. Twigs looks into the camera. "My thighs are apart for when you're ready to breathe in," she promises.

This is the video for Two Weeks, the first single from twigs's debut album, set for release this month. With her iconic styling – a mix of thuggish leather, gothic lace and occult bling – alongside songwriting that blends darkly spectral production with beautiful melody, she's being lauded as a visionary new voic. She's also a pop star who really nails sex. For a culture so obsessed with carnality, songs that get it right are bizarrely few and far between: Madonna's Erotica, perhaps, or Marvin Gaye's I Want You, whose lyrics seduce while the music is already biting the pillow. Twigs, however, is writing strings of them; sex in her songs is a shifting game of sustain and release, a far cry from the seaside postcards of Perry, Cyrus, Thicke et al.

"I write exactly what I think," she says of this frankly hot material when we meet. "If it's a raw subject, I write lots of things and then pull out all the fluff words." Hence Two Weeks, a song about wooing a man away from a sexless relationship, features the line "I can fuck you better than her". "Weird things can be sexy," she continues. "Vulnerability is the strongest state to be in. How boring would it be if we were constantly dominant or constantly submissive? In the video, it's this vision of me feeding myself, milking myself. I was naked, painted in gold, doing krump dance moves. It's bizarre, but hot in a very weird way."

FKA twigs: this week's Guide cover feature. Photograph: Dominick Sheldon.

She goes on to talk about another of her songs, Papi Pacify, the video for which shows twigs wrapped in a perpetual embrace of ecstatic submission. "Everyone's like, 'Oh, it's so shocking', but you were doing it last night," she says. "If I was a mother, I would rather my child watch a video like that and not understand it and be inquisitive about what it means. Be curious about something that's so complicated, rather than watch something really crude and overtly sexual." She says that we live in a culture where "being sexy" is a mendacious, exhausting bind for many women. "You have to be a size zero, but real women have curves. But when you're curvy you need to watch your BMI and your cholesterol, so you need to lose weight, because strong is the new skinny. It's so confusing. I'd rather be experimenting with intelligent sexuality, which I don't know yet, I'm only 26. I've had two or three serious relationships, I haven't been married, I haven't had that ultimate relationship where something clicks and I'm like, 'I get it now!' I'm still learning."

We're in central London, in the pretty unerotic environs of a chain restaurant, but twigs remains obviously strange, a compact arrangement of eyes, biceps and goofy teeth. Those peepers grow and flash with irritation when I mention how much of the coverage of her music has seen her boxed alongside "alt-R&B" stars such as Banks, Kelela and SZA."It's just because I'm mixed race," she interjects. "When I first released music and no one knew what I looked like, I would read comments like: 'I've never heard anything like this before, it's not in a genre.' And then my picture came out six months later, now she's an R&B singer. I share certain sonic threads with classical music; my song Preface is like a hymn. So let's talk about that. If I was white and blonde and said I went to church all the time, you'd be talking about the 'choral aspect'. But you're not talking about that because I'm a mixed-race girl from south London." She gives me a look as if I've asked her to take the restaurant's bins out.

In an attempt to placate her, I ask if she feels singular. Her face softens. "Very. I love annoying sounds, beats, clicks. Kakakakaka!" Her hands wave violently around wisps of Afro that have escaped her do. "I don't see anyone else doing that now. It's got loud noises in there, the structures aren't typical, it's relentless. It's like punk; fuck alternative R&B!"

Tahliah Barnett began her career as a dancer. Growing up in Gloucester as the only mixed-race girl in her Catholic school, a natural rhythm propelled her to childhood classes and through to an eventual career throwing shapes for pop stars; the click her bones made when in motion prompting her stage name. Her clients included Kylie Minogue, whom she worked for even as her own EP2 was getting serious notice. "It was incredibly humbling," she says. "It's really good to be in one environment where everyone's like, 'Twigs, are you OK, can I get you a glass of water' to another environment where you're one of 20 backing dancers in a cold room and no one's fed you for five hours." She also danced for Jessie J, Taio Cruz and Plan B, whom she describes as "a sick, actual artist. He's so involved: there at 10am explaining how he wanted each of the dancers to have their own character."

She sets this positive experience first against much of the world of commercial dancing. "Usually it's just 'look hot and wear hotpants'. You go to dance school, you train your arse off for five years, you can do a triple pirouette on your head and land in the splits, and then you come out and someone's like: 'What are your measurements?'" It's a long way from Josephine Baker, the dancer who scandalised Paris in the 1920s with her nearly naked routines, and whom twigs admires. "She's saying: 'I'm doing this and it's for me.' She's giving to the crowd, but ultimately she's enjoying the way she moves, and her love is in the movement. Nowadays it's: 'I'm going to shake my arse like this, and it's for you, to make you feel a certain way.'"

FKA twigs Photograph: David Burton.

Twigs rails against this "bizarre time in the world, where you can be so famous, so elevated, but none of it is your own vision". She herself refuses to give up creative control and, in fact, is determined to extend it wherever possible. Take the production on the album. Punk was what she grew up on, and initially tried her hand at, "but I'm terrible at shouting. It wasn't me. I was just trying to fulfil my Poly Styrene fantasies." Instead, she taught herself the software package Ableton and has numerous production credits on her album, alongside Kanye fave Arca, Dev Hynes, Sampha, Bruno Mars and Eminem producer Emile Haynie, plus Paul Epworth, the Oscar-winning Adele collaborator. All were picked for their ability to "fill in my blanks, in things I'm not good at". Sampha helped with chords, conjuring specific emotions like feeling "brooding but with an underlying hope, but mainly depressed"; Epworth helped with "structure". She has also taken control of her music videos, which she's now directing with production company Academy at her back.

"I like that she knows what she wants," says Nabil Elderkin, a director who worked with twigs on Two Weeks and has also shot videos for Nicki Minaj and Arctic Monkeys. "She doesn't sacrifice anything for popularity, she just comes in and does it her own way. That's how some of the best artists today work: Kanye West, Bon Iver, James Blake, Frank Ocean. And twigs is exactly the same thing. She has imagination and art and puts it out how she wants. She's in control of that 100%."

While she gets to be submissive in her personal life ("I'm like, 'Bagsy being little spoon!' every night"), this domination of every aspect of her career is proving a tiring business. But, to wring out the metaphor, she can go all night. "I'm exhausted, but whatever," she says. "Now is the time to be doing it, and as long as I'm happy I'll keep on doing it. But if I'm unhappy, I'll just disappear. I will shave off my hair and live in the south of France, and I'll be learning a new language where no one gives a shit about who I am. I need to be happy."

FKA twigs's debut album LP1 is out on Young Turks