Natasha Khan: rocking 30s style

Last year, while she was getting ready to release her third album, Natasha Khan – better known by her nom de pop, Bat for Lashes – cut her long, thick, dark, wavy hair into a neat bob. This was universally taken to be a sign, since Khan's hair had previously been styled around motifs of wilderness, madness, rebellion. Sometimes it was long and loose, all the better for a pagan whirl on stage; sometimes it was topped with a Native American-style feather headdress. For a while there had been a glittery headband, motif of those ultimate good-time girls, the flappers; once there were two tiny white feathery swans nestled in the dark hair in a Björkian echo. The bob, it was assumed, heralded a new clean-cut, grown-up persona.

"Actually, I cut my hair because I was getting really bad split ends," Khan says, and bursts out laughing over her vegetarian focaccia. This vegetarian focaccia has already caused a crisis in the Victoria Park deli where Khan has asked to meet. The success of her albums – Fur And Gold in 2006, Two Suns three years later and now The Haunted Man – has seen her crowned as art-pop royalty, Victoria Park's version of the Duchess of Cambridge. When it turned out there were no avocados for the salad Khan ordered, a waiter was hastily sent out to buy some. He returned, empty-handed and aghast, reporting that "there are literally no avocados in the village", his stricken expression neatly encapsulating how mightily things have changed in the E9 postcode and how much hipster boys (and girls) crush on Khan.

The Haunted Man, released just before Khan's 33rd birthday, is, she says, "very much the woman of my album trilogy. The first album is little-girl Natasha – suburbia and horror films and that crazy internal life of adolescence. The second was me going out into the world, having an incredible time but kind of out of my depth in love and hate and craziness. With the third one, I had calmed down a bit, stopped flinging myself around between dramas. It's more subtle. It's about the complexity and nuance of how a woman in her 30s feels. All these possibilities: feeling broody or maternal or nurturing or sexual or powerful or angry or frightened or forgiving."

Khan may be older and wiser, but she is still (as she puts it succinctly) "badass". Her bob, while undeniably no-nonsense, is less Michelle Obama than Zelda Fitzgerald. On the cover of The Haunted Man, she appears naked, with a naked man slung over her shoulders. The idea came from a photograph by Ryan McGinley, in which a naked girl is carrying a wolf in the same pose, which Khan came across in a book halfway through the making of The Haunted Man. "This album is about relationships, about men and women, and I imagined the man as a soldier, or a sailor I had dragged in from the sea." She approached McGinley about revisiting the idea, and he agreed.

There is a magical element to the cover, this slender girl with a man slung over her shoulders, that plays into the tendency to file Khan under kooky. But despite the vaguely mystical image that hangs around her, she is entirely clear-eyed about the difficulty of her position in the musical marketplace. "The record company doesn't know what to do with me, because I'm not a Lily Allen, but I'm not really an indie artist, either. All the best artists have been in the middle. David Bowie worked with Brian Eno and dressed up in extraordinary clothes, but he was also a brilliant songwriter who captured the thoughts of a generation. He was hugely successful, without compromise. So, that's the dream. But you only have to turn on the radio to recognise how much the musical landscape has changed." Sometimes, she says, it's tempting to "get a big remix done, or whatever. But it comes down to an ethical decision about whether it feels right, and I know selling out won't bring me happiness."

The Bowie analogy is a telling one. It frustrates Khan when the visual and storytelling elements to her performance are patronisingly batted away as the vague hippy-dippiness of an art-school chick. "In the music industry, intelligence in women is undervalued. What pisses me off is that I write my own music, do the production myself, then get written about as a singer who gets dressed up. In the art world there are these extraordinary, vivid, strong female personas – Louise Bourgeois, Cindy Sherman, Yoko Ono – but music won't allow women the space for that."

For her most recent tour, Khan took sketches of her own designs to her dressmaker: Martha Stewart dancewear shapes, in monochrome, with graphic lines. "The look was conceived in a more deliberate way. Before, when I was in New York with my boyfriend, we'd make an art project out of going round the thrift shops, finding these amazing juxtapositions, like gold antlers with a pair of boxing gloves." Today, she is wearing a vintage fake fur jacket she found in LA, an Anthropologie jacket and a YMC jumper in Pepto-Bismol pink. And she is collaborating with Australian fashion duo Romance Was Born, who are making outfits for her next tour. I am quizzing her about these stage clothes and Khan, in her typically left-field way, starts telling me she has a new boyfriend, an actor. "When I look at this man, who I've just fallen in love with, it's like looking at a rainbow. So when I'm on stage, I just want to wear rainbows. I said to [Romance Was Born designers] Anna and Luke that in my head I can see a white cape with gold edging and cuffs, and maybe a rainbow onesie underneath? And they're like, cool, no problem, we'll sort it."

She looks suddenly radiant, smiling at the thought of the actor, the rainbows, the designers who unblinkingly catch her curve balls. "The impulse for everything comes from a very personal place," she adds. You don't say.