I don’t know anyone who has a bad word to say about Maggie Gyllenhaal. Sometimes we, the viewing public, can be unkind about ladies in the spotlight, but, for some reason, she isn’t a target. Is it that funny look in her eye that suggests she is in on the joke? Is it how, in pictures of her at premieres, even when she is dressed in a fabulous frock, her hair often looks as if she has come straight from the gym? Is it because she has a fit brother?

Whatever the reason, every boy I know seems to want to sleep with her and every girl I know seems to want to have a cup of tea with her. I have high hopes for our lunch, which is taking place at Nobu, in downtown New York. I’m secretly thinking we could become friends.

Gyllenhaal is late, so I use the time to slip off to the ladies and splash my face. (It’s stinking hot outside.) I get back and she is there, sitting at the table, smiling widely, taking my hand and saying, “Haven’t I met you somewhere before?” Yes! No.

She is wearing black short shorts by Isabel Marant — an NY-hipster staple this summer — which make her pale legs look paler, with a green string vest she says she has had since she was a teenager. Her hair is fluffy, as if she really has come from the gym. She chose this particularly chichi restaurant because she liked the thought of “a nice lunch on someone else’s dime”, but isn’t actually that hungry. She and her fiancé (the actor Peter Sarsgaard) have had a bug all week (although not their two-year-old daughter Ramona: “Thank God”) and it’s her first meal out.

Heath Ledger tipped for Oscar

Black carpet rolled out and talk of a posthumous Oscar at the unveiling of Heath Ledger film The Dark Knight

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BACKGROUND

• Final farewell to Heath Ledger

• Batman Begins

• Who is the best big-screen comic book hero?

Related Internet Links

• 10 things that make Dark Knight the best Batman ever

• Interview: Batman's Special Effects wizard

• Batman Begins: Blu-ray competition

We do the preliminaries, then talk about the new Batman film, The Dark Knight, Gyllenhaal’s first blockbuster. It sees her make the transition from indie queen to multiplex goddess. It’s brilliant, partly because of Gyllenhaal, of course, and partly because it stars Heath Ledger as the Joker, who is so good that posthumous Oscar nominations are already being discussed — sometimes by people who haven’t even seen the film yet.

Gyllenhaal, 30, plays the female protagonist and love siren, Rachel Dawes. She replaces the anodyne Katie Holmes and her perma-cute “Oh”s. Gyllenhaal’s Dawes doesn’t do “Oh”. She is far more complicated and accomplished than that. Rather like the woman who is sitting here, watching me expectantly over her menu. A quote I’d read comes back to me: something about someone asking her little brother, Jake, to say five words about her and him replying, “Can I have six?”, and then saying, “She is not as she seems.” Well, he should know.

Indeed, she is charming, articulate and twinkly — yet rather distant. When the waiter interrupts four, five, six times with random questions and the offer of complimentary film-star treats, she says, “Great. Thank you very much.” In reality, she is miles away.

In common with many A-listers who are more luvvie than pay-per-view show pony, Gyllenhaal is a prolific interviewee (“I don’t like it, but I’m happy to do it if I have an interesting project to talk about”), but one who specialises in not actually revealing much. You have to earn her trust. So when I ask her what she enjoys doing when she isn’t working, she tells me that she focuses a lot on her relationship and spending time with her two closest girlfriends. “And going to the theatre, films . . .”

The movie that got boys fancying her was Secretary, a black comedy about a self-harming ingénue, whose S&M relationship becomes a sexual awakening that turns out to be her salvation. Gyllenhaal expected outrage of the “old-school feminist” kind for her portrayal of a submissive female with a taste for spanking, but received only plaudits. In retrospect, it could only have been that way: she would never play that kind of sex object. She is well-read on feminism and gender politics and says the worst thing that ever happened to her was a male television presenter telling her he had fast-forwarded to the sexy parts of Secretary. The advertising campaign she did for Agent Provocateur last year made the same point: the expression on her face, as she sat there in a basque, brushed off the idea that frothy underwear is for male pleasure only.

So The Dark Knight will make her globally famous — more famous than the famous she already is. Which is possibly more famous than she would like to be. It is well documented how disgusted she is by all the paparazzi attention. In one incident, they photographed her breast-feeding. In another, they tried, outrageously, to flush her and her baby out of their home (a 3,600 square-foot, four-storey townhouse in Park Slope, Brooklyn, with — or so I read in a newspaper snippet — “seven marble fireplaces and a charming, delightful, well-established garden”) by calling the fire brigade. She and Sarsgaard are contemplating a move out of town. “I don’t court it [the attention] at all. I don’t like it at all. I don’t want it at all,” she says. “I hope that if I talk about it enough, it will go away. I’m very protective of my life.”

Plainly, this is because Gyllenhaal grew up in Hollywood (scriptwriter mother, director father) and is ambivalent about the attention. She knows the deal: how you can be smokin’ one minute and a nobody the next. She is quite practical about it all. I think she has worked very, very hard to get where she has. “There is only room for five people at the top,” she says. “Mainstream Hollywood makes a few good movies a year, and in order to be in one of those, you have to be one of five people.”

Hence Batman, over which she wrestled with her conscience.

“I do want the power that comes with celebrity, because I have good intentions,” she says. “I feel as if I could do something good with that power.” But also, there is the big question: if you’re a mother, how far do you take it? “My fiancé is so supportive. I was thinking of doing a film on an island off Tasmania, and he said, ‘Great, I’ll come and take care of our daughter.’ ”

Jake says she isn’t as she seems. She is a scruff today, but she scrubs up beautifully. She can work the silk blouse, pencil skirt and heels look with the best and can transform herself into a proper grown-up movie star — the one you see in these pictures. But being a bit of a mystery doesn’t give her a get-out-of-jail-free card for the paranoia that comes with the job.

“I’ve been lucky to have escaped the worst of it,” she says. “But it would be doing everyone a disservice to say that I feel good about myself all the time and that I never think I look bad or that my hair looks awful. If you think you’ve got bad hair, try going on a month-long press tour with it!”

We have almost finished our blackened cod, and I think she might be hoping that we’ve covered everything. (“Are you done?” asks the waiter for the umpteenth time. “Yes,” says Gyllenhaal. “Not quite,” I say. “Okay, no,” she says.) Anyway, we haven’t.

Batman is a knockout film and it belongs to one man: Ledger. We know that. The film company, Warner, knows that. The cast know that. However, Warner has explained how understandably less than keen the cast are to discuss him. It must be particularly difficult for Gyllenhaal — her brother was nominated alongside Ledger for an Oscar for Brokeback Mountain. I do it anyway.

“Heath . . .” (Ouch.)

Long pause. Gyllenhaal swallows. She looks stricken. She hates me. Eventually she says, carefully and looking down: “He was a fantastic actor, and he was great to work with.”

Another silence. “Is that the time? I should go. Thank you so much for this. It’s been great.” A grin, a wave — and it’s as if she was never here.

The Dark Knight is released on Friday

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