Martha Wainwright: Why do I get all the nerds?

Will you look at the legs on Martha Wainwright? On stage at the Royal Festival Hall, London, where she is beginning a short tour that will take in a couple of summer festivals, she is wearing cranberry-coloured shiny leather boots, a black froufrou mini-skirt and no tights. Strong and braced beneath her, those legs have a life of their own. While her vocals soar, effortlessly powerful – one critic recently said that of all the singing Wainwrights, Martha is the one with "the voice" – she scrapes her left foot on the stage repeatedly, like a pony, then kicks it back ecstatically as she hits a top note. Sometimes, in intense moments, she throws a full-on knee-trembler, Elvis in froufrou skirts. It's enough to give a straight woman a crush. Best of all, she barely seems to know she's doing it.

"I know I'm very physical on stage and I think that helps push out the songs," she says to me the next day, sitting in a tracksuit in her publicist's boardroom. "I move around a lot, I have a lot of nervous energy... But is it sexy? I don't feel totally great about my face or my body and I certainly don't want to use sex to get ahead. As a female I'm not very coquettish, so I guess the sexuality comes out in a strong way, in a way that's open about being needy and being sexual and being humanistic. So, y'know, it's not often the sexy handsome guys are attracted to that; it's the little nerdy guys who come up to here" – she makes a this-high gesture, warming to her comic theme – "so that when you're dancing with them, their heads are on your chest. Ha! But it's OK, these guys are... smart."

She's droll. It isn't what you necessarily expect from a singer whose cover of "Stormy Weather", recorded at her brother Rufus's Judy Garland tribute concert, is the most grief-drenched, tremulous version you've ever heard. But that seems to be the deal. She wants to break your heart and crack you up.

"I don't find it sexy when I come off stage beet-red with make-up streaming down my face. I'll let people find that sexy if that's helpful to them. It's not a look that's helping me get laid. Not that I need that any more, 'cos I got married." Indeed, to Mr Brad Albetta, who produced both her albums and plays bass in her band. He's a little older, a supportive presence on stage, watching her from under a bleached blond crop the same shade as Martha's wild yellow barnet. Exactly the same shade, in fact – "We shared the peroxide. After I was done I finished up the bottle on him.

"A journalist in Copenhagen said something about Brad that was very astute," she adds, astute coming out "astoot" in her Montreal-born, Brooklyn-based accent, a voice that's musical and emphatic and ironic all at once – "which was that he's proof the modern man really does exist. He's very helpful and willing and generous to allow me to go on stage half-naked and shake my ass and sing songs about my past loves."

Listen to 'You Cheated Me'

Taken from the album 'I Know You're Married But I've Got Feelings Too'

Her new album has the darkly comic title I Know You're Married But I've Got Feelings Too. After the show, you can buy a pair of pants with these words emblazoned on them, an exquisitely sick merchandising joke. Fans' knicker drawers may also contain a pair with the title of her first hit printed on them: "Bloody Mother Fucking Asshole".

"That's typical of her sense of humour," says a friend. "She's into quite a lot of British shows. She loves Nighty Night and The Mighty Boosh."

The single "Bleeding All Over You" (that one, thankfully, doesn't make an appearance on any pants) describes a pre-Brad infatuation with a married man, an affair which was, she stresses, "unrequited – I'm no home-wrecker!" When she's performing on stage or singing for herself, none of that matters anyway, not the husband (someone else's) who inspired the song or the husband (her own) playing bass. None of the rational stuff matters at all.

"What you're really trying to go for is that feeling of freedom – God, please don't think of George Bush when I say that word – that feeling of freedom, of soaring, the closest thing that we human beings might have to the feeling of flying. That's what the track "I Wish I Were" is about, about how much I just want to be in that impossible moment where, y'know, time stands still and everything melts away, where the senses are completely open and the mind stops working and there's no fear and no paranoia and no pain. A moment of total bliss. That's the ultimate goal." Does she ever achieve it? "Hopefully at least once in a show."

Listen to 'Bleeding All Over You'

Taken from the album 'I Know You're Married But I've Got Feelings Too'

When Martha was in the womb, her mother, the folk legend Kate McGarrigle was in top flight, writing and performing songs such as "Go Leave", addressed to her husband, Martha's father, the equally legendary Loudon Wainwright III, who had recently run off to Europe with the performer Penny Arcade. Her parents separated officially when she was one. "I'm a victim of divorce... No, I'm not, I'm a child of divorce – knowing both my parents, I'm glad they don't live together. Brad and I are both children of divorce and I don't think we want to do that."

One of her early memories is the Newport Folk Festival. "My father invited Rufus and me up to sing 'Dead Skunk'. There's a photo of us – I was about eight, looking very composed with a straight back, and I remember standing there thinking, 'I like this.'" Summer holidays they spent performing with one parent or the other. Discipline levels were high. "When you sang with Kate and Anna [Martha's aunt] you had to have your part dead right... It wasn't the Von Trapp family."

Martha and Rufus lived in Canada with their mother, and she studied drama at Montreal 's Concordia University. Then she moved to New York and began her wilderness years, years spent "writing little songs and drinking and being a fuck-up". As she told John Walsh in The Independent three years ago: "I've frolicked with the Bohemians at the bottom of the barrel."

Mercedes Grower, a British actress, was there too. She was taking acting classes in New York and living in a railroad apartment in Brooklyn when Martha, a friend of her flatmate, kept turning up at the door in jogging clothes. "Then she asked to move in. We connected quickly, in the way that girls can do, and the three of us turned into a sort of dysfunctional family, camping out like dirty little tinkers. There was art stuff everywhere and you had to walk through Martha's bedroom to get to my room, which was in, like, a side toilet. I made our flatmate a bed in the kitchen, with a curtain of papier-mâché puppets, as he was drinking then and never made it to his own bed. It was really hot and we had no air-conditioning so we just walked around naked a lot and took cold baths. It was ridiculous but it felt OK living like that because we were all new to it, just starting out."

Grower worked in "some trashy bar" while Martha kept herself afloat doing gigs. "She was singing and writing all the time," remembers Grower. "I'd wake up and she'd be singing. It's just what she does. If she hadn't made it, she'd be singing every night in a bar in some back-ass town in Mexico, standing on the table with her skirts up, singing her heart out. And then cooking everyone a feast afterwards at five in the morning. She cooks as good as she sings."

Grower, who was a bridesmaid at Martha's wedding last year, describes her as sensual, erudite and generous. And a natural exhibitionist: "When she's had a few too many drinks she'll get up and do a wild improvisational dance. Sometimes she'll drag her mother in and it all goes a bit..." Searching for the right comparison, she hits on the Maysles brothers' mad mother-daughter documentary: "A bit Grey Gardens."

For five years during her twenties, Martha struggled to get a record deal that suited her. "I was too much of a wild card," she says. Personally? "And musically. And not fully believing I could do it..." Understandable, given her family's achievements. With her brother's extravagant success and captivating egomania ("I am great and that's all there is to it"), the bar was set, she says, "pretty fucking high". Still, "It got to the stage where I needed to make a record and I was ready and it was embarrassing that I hadn't."

She started to finance her own recording sessions but ran out of money "after two days or whatever". Enter Albetta, whose previous producing credits were young artists including Teddy Thompson (son of Linda and Richard). "He said he had a studio and we started working together and he really pulled that record together and made it happen and pushed me and helped me."

Will a happy marriage take away her best subject matter, tortures of the heart? "God, I hope so. No, I think sexuality and feelings of inadequacy are normal, married or not. I realised I needed to be loved and that I was tired of running after people who didn't want me and where it wasn't working... Him falling in love with me – and I say he did, I think he did, he might not have – him falling in love with me and taking care of me was very helpful to me." And the chemistry between them grew slowly? "I liked him from the first moment I saw him, but, you know, nothing is ever easy with me."

Martha talks of her husband as her "ally" outside her family. "He was the only person I'd really met who took me out of the, er, the algebraic equation that is my family, y'know, if Rufus is here and Kate is here and we put you here, then that equals what? He reminded me that I exist without these people." She refers to her parents by their Christian names now – "except," she laughs, "when I want something."

"Obviously, I don't exist without my parents, who made me, but I have recently got to a place where I have been allowed to be myself and I feel as though there's a propulsion forward and that everything can work out for me and I won't be a failure."

She says this with her second album receiving rave reviews ("a masterclass in complex sophisto-pop", "Martha comes into her own" etc). Debuting at 29 in the charts, it may be more a critical than a commercial success, but still, she's everywhere. On the afternoon I meet her, she is being tugged in 10 directions at once: hair, make-up, radio, TV... Usually when she's in London, she spends time with friends the singer-songwriters Beth Orton and Ed Harcourt, eats oysters at The Cow in Westbourne Park or swims with Grower at the Hampstead ladies bathing ponds – "Topless, of course. Until they banned it. They should give us a break. If you're going to get chewed up by little water rats you might as well be able to take your clothes off..."

She tells me that last night, after appearing on Later with Jools Holland, she sat in front of the televised Commons debate about abortion, "watching them counting the yays and the nays" as MPs voted to keep the time limit at 24 weeks. "I think they came to the right decision," she says. She had an abortion at 18, but now, at 32, wants children. "I'm really, what's your word for it? Broody. That's why I got married. You have more rights if you're married and so do your children. I have hopes for doing it in a structured way."

The idea that if she has children, they will listen to her music suddenly hits her. "I feel bad now for all the terrible things I've written. My mother and my aunt's music is the soundtrack for my life and it's much more tender than mine. My songs are... not lullabies. They're rock'n'roll lullabies!"

For the first time, she says, she is writing outside her personal experience. There's a delicate, tentative anti-war song on the album, called "Tower", as well as a meditation on death, "In the Night", inspired by her mother's brush with cancer. "But I didn't want to use her or the particular details of her cancer in the song because I felt that would be exploitative. The songs have to go beyond their subject matter. That's a lesson I learnt from 'Bloody Mother Fucking Asshole', because when I told people it was about my father, they really ran with that and I think it hurt him.

"I'm learning to be less selfish and I'm doing less navel-gazing." Shortly after saying this, she chats to her make-up artist about how one of her eyes is fractionally differently shaped to the other one. "Aren't everyone's?"

For all the progress, elements of her life are still "insecure": "My ceiling is falling down. Our apartment in Brooklyn is a dump; in fact, I'm considering squatting." Still, with a huge Venetian chandelier (a wedding present from Rufus) hanging over a grand piano, it is a romantic kind of dump. And in the middle of it is Martha, questioning and confident by turns, partly humble, partly proud, all talent, all truth.

"I think this is quite selfish and egocentric as a career choice and the only way to offset that is to give as much as I can on stage. To offer something up... I want to be part of the evolution of music as a whole, not to copy from the past but to bring something new along myself. And what else can I do in life? I don't have any other skills."

'I Know You're Married But I've Got Feelings Too' (Drowned in Sound) is out now. Martha Wainwright will appear at the Glastonbury Festival on 28 June and Latitude on 18 July