Cyndi Lauper is not one to take a compliment lying down. Introduced to her in her suite in a London hotel, I say she looks fantastic, but only because she does. She is petite, with two cream orbs that erupt from her tight velvet top. Her face is so smooth and white that it looks as if it has come off a production line at a Victorian doll factory. Her hair, which at the peak of her punkish fame came in any colour of Liquorice Allsorts, is as fair as her skin, but mixed with a hint of honey. “I’m old,” she returns my praise, “not dead.”

Alive and kicking, I’d say — and my shins are bruised often as the 52-year-old pop star and I fight for control of the 60 minutes we share. She is determined to tell me about the mates she got to play on her new album, The Body Acoustic, and about how she has used the dulcimer, an antique-sounding string instrument, on it. (The word “dulcimer”, incidentally, is as near as she gets to the word “dulcet” — she speaks the Queen ’s English as in Queens, NY; think of Miss Adelaide from Guys and Dolls.) Body Acoustic is a likeable record and includes unplugged versions of the Lauper classics Time after Time, All Through the Night and, yes, Girls Just Want To Have Fun, the 1984 song we still love her for. But, to be honest, I am more interested in hearing the story of an extraordinary life that took her from an abused childhood to the edge of destitution, briefly made her bigger than Madonna and left her, before the current redemption, in the wilderness.

As a compromise between discussing her life and her art, I ask about the domestic mood of The Body Acoustic. If her 2003 album, At Last, marked her torch-song period, this is her porch-song record. The accompanying DVD has many songs played on a wooden veranda. Is this, I ask, because she is a mother now and has warmed to homely values? “Homely values,” she spits. “Please don’t confuse me with who got voted in. And don’t blame it on a New Yorker. I didn’t vote for Bush. Nobody in New York voted for Bush.”

It is true that her President would probably not be willing to endorse She Bop, a song in praise of masturbation. “Well, guys are always singing about it. I always felt like whatever guys can do, why can’t I? If you don’t want me doing it, don’t do it yourself.”

I congratulate her on daring to celebrate such a harmlessly pleasurable act. “I’ll think about that when I next shake your hand,” she says.

One can’t blame her if she is suspicious of families: she came from one that lodged in the shadow of the Singer sewing machine factory in the wonderfully named Ozone Park, Queens, and was a model for nothing. Her father, Fred, a shipping clerk, took off when Cynthia was 5, leaving her mother, Catrine, a frustrated musician, to raise three children on a cocktail waitress’s wages. Cyndi felt that her mother’s life had been wrecked by her own father, who had denied her an education. She hated the macho bully Catrine then married even more. This was Italian-American domestic hell. “Immigrants,” she says. “They were treated badly. When someone’s treated badly it’s kick-the-dog syndrome. They get kicked, so they kick the dog.” Or the wife? “Right. Then the kid kicks the dog. I burnt ants with my flashlight for about one second.”

Her 1993 album, Hat Full of Stars, included Lies, a song about incest. I ask if it is true that it is autobiographical. She does not deny it, but resents her record company for trying to make it a selling point. Incest, she says, is about respecting or flouting boundaries. “Those are my boundaries: I don’t want to talk about that for public display.”

Unhappy at home, she was unhappy at school, too, and by the age of 10 had been expelled from four schools, including a convent, whose unsympathetic teaching staff, disapproving of her divorced parents, later prompted Lauper’s comment that nuns were Nazis and the Catholic Church was organised crime.

The short of it is that by her teens Lauper was a “recovering Catholic” and a committed feminist. “So many things didn’t make sense to me that I decided it was all a load of crap and I was going to live my life like a man and have the same civil liberties.”

Does she worry that younger women often seem to view the feminist movement as irrelevant? “That’s just until they find their rights taken back, then they’ll really stand up and get pissed off, because all the people shooting their mouths off saying ‘I’m not a feminist’, they’re lawyers. They wouldn’t be lawyers if it weren’t for feminism.”

At 17 she ran away from home, though she says she had been mentally packed since her 14th birthday. For a while she was homeless and was treated in hospital for malnutrition. She worked as a social worker, a model and a “geisha” in a Japanese piano bar. She played in cover bands, but then a vocal cord collapsed and she was silenced. “They kept saying ‘Drink this Southern Comfort, Joplin drank it’, and I kept saying, ‘Yeah, but Joplin’s dead ’.” The voice recovered but finding work was still tough. Club managers objected that she moved like a boy (she still worries about her dancing and thinks she walks like a duck). Then, when she was 24, she met the pianist John Turi and they formed a group, Blue Angel. The association ended badly, however, and her manager, claiming breach of contract, took her to court to prevent her performing elsewhere. A judge eventually ruled: “Let the canary sing.”

In 1984, a year after she filed for bankruptcy, Lauper made her first solo album, She’s So Unusual. It sold nine million copies and contained four hit singles, including Girls Just Want to Have Fun. As is often noted, that summer it wiped the floor with Madonna’s Like A Virgin. It looked, at last, as though Lauper was having fun.

“My life did change radically. I thought, ‘OK, you’re set’, but I wasn’t so set, because while everyone else was having fun I was going back to my hotel room doing my voice exercises. I was alone and people just kept isolating me — ‘Oh, Miss Lauper, we’ll sit you here; no one will bother you’, and in the other room you’d hear them all laughing and having a great time.”