Paltrow wants privacy, and she's not kidding: this week she and her husband, Coldplay frontman Chris Martin, took legal steps to ensure pictures of their daughter, 19-month-old Apple, could not be published in the press. A snap of the little girl in pink ear-defenders during Coldplay's Live8 set is the closest Paltrow gets to a public mother-and-daughter photo opportunity.

In London, where the Martins spend more than half their time, in a two-storey Georgian house that used to belong to Kate Winslet, she admits that she has become a paparazzi-buster, taking pictures of cars if they get too close and noting their number plates. "I can go to the police," she says. "I know my rights. And, believe me, I will have them arrested. I'll stop at nothing."

Consequently, as we sit in a bright London hotel room, one of us is self-consciously maintaining very steady eye-contact, in case a dropped glance stomachwards is misinterpreted as another kind of covert press intrusion. Yet here is a paradox: the limelight of celebrity is responsible for bringing Paltrow the things she loves best. Through fame, she has interesting work, close friends such as Madonna and Matt Damon, homes in London and New York's Tribeca district, and a husband.

Paltrow met Chris Martin at a Coldplay VIP after-show party. Their relationship became public six months later, in August 2002, when he dedicated his hit song 'In My Place' to her at a New York concert. In December 2003 they eloped to California. They tied the knot with just a few friends present when she was several months pregnant with Apple.

Martin was not her first high-profile alliance, of course, and in the past Paltrow has been visibly irked by the fact that it has often been her starry boyfriends, not her films, that have catapulted her into the headlines - first as the fiancée of Brad Pitt and later on as Ben Affleck's squeeze.

Shakespeare in Love changed all that. As Shakespeare's muse, Viola De Lesseps, she captured an accent, acclaim and an Oscar. After that, she hit fifth gear, working almost non-stop in films such as Shallow Hal, The Talented Mr Ripley and The Royal Tenenbaums. Her status as a star seems unassailable, even if her films' box-office success has been inconsistent and the personal benefits not entirely clear. "When you reach the pinnacle of your success at 26 years old, as I did, it's not very healthy, because it leaves you in a sort of crisis in terms of what you're supposed to do for the rest of your life," she later admitted.

Success arguably arrived even earlier than that. Paltrow was born into showbusiness aristocracy - her mother is the acclaimed actress Blythe Danner, and her father, Bruce Paltrow, built a successful career as a television producer, most notably with the series St Elsewhere. This would prove to be both a help and a hindrance to her career. "I felt like I had to work much, much harder than a lot of other young people to prove myself in this business. Other people could come out of nowhere. I felt I had to work harder to get the respect that everybody else seemed to get," she says.

On the other hand, her background gave her a hotline to the kind of hunk actors other teenage girls could only stare at on bedroom walls. "I do remember having a crush on Keanu Reeves," she chuckles. "And my mother worked with this make-up artist who was going out with him. So they took a Polaroid of him and he signed it for me, but then I just felt retarded. It kind of ruined it."

Despite her cool-cat poise today, 33-year-old Paltrow has another kind of career crisis. Her new film, Proof, is her first in two years, and while she carefully praises cast and crew, she also says, "I don't really work very much any more. Since having Apple I've done two films, and each part was only 12 days long."

Her ambitions, she admits, have shifted from the professional to the personal. "Everything I wanted to achieve, I achieved," she shrugs. "I'm not one of those people who keeps raising the bar. Am I supposed to say I'm going to become the biggest movie star that ever lived? I don't want to."

In 2002, Shakespeare in Love director John Madden invited her to play the lead in the London stage production of Proof at the Donmar Warehouse. But in the four years between appearing on stage and the release of the film version next month, Paltrow's life has changed completely, with marriage and the birth of her daughter. Particularly harrowing was the unexpected death of her adored father, Bruce, while he holidayed with his daughter in Italy - an experience that lent all sorts of uncanny resonances to her character in Proof. In it Paltrow plays Catherine, a once-promising maths student who drops out of college to care for her father, played by Anthony Hopkins. After his death, Paltrow's character is left alone with her own demons to fight.

Bruce Paltrow was devoted to his daughter, whom he directed in his last film, Duets. When she was 12, he had taken her to Paris, "because I wanted you to see Paris for the first time with a man who would love you for ever, no matter what", she explains.

"My relationship with my father was the most central relationship of my life from the time I was zero to 30," says Paltrow. "The first anniversary of my father's death was right in the middle of shooting Proof. I wasn't in a great place emotionally in my real life when I was doing the film. I was pretty bereft. I was also newly pregnant and I felt really, really sick."

She tries to laugh at this memory, but does so awkwardly. "It wasn't like, 'Oh, the day is done' and going out for a nice meal or something. I couldn't even have a glass of wine. I'd just go back to my hotel and eat a sad grilled cheese sandwich and watch something depressing on television."

The bleakness she felt during the making of the film undoubtedly fed into a performance of rawness, uncertainty and insecurity that is piercing. Paltrow and the dramatic revelations retained from the play make Proof an absorbing film, despite other drawbacks.

Sir Anthony Hopkins was impressed by his co-star's ability to get the job done despite her bereavement. "When I watched the rough cut of the film, it crossed my mind that it must have been quite painful for her to do that role at that particular time," he observes. "But I found her very uncomplicated. She arrived on the set on time, she did her job. She's very practical about the acting business. I like that."

This self-contained discipline has backfired on Paltrow in the past. Her two-hour sunrise yoga sessions and macrobiotic diet (though hers appears to include wine and cheese) have been held up as instances of fussy obsessiveness. In fact, this behaviour had everything to do with her father. Paltrow credits her parents with imbuing her with the professionalism, careful politesse and compulsive punctuality for which she is known.

Despite her reputation as a frosty personality, though, in person she is cool rather than cold - although she has an unnerving trick of frowning quizzically at questions, even ones of yelping obviousness or banality. Such as: how was your maths, Gwyneth? "Erhmmmm? Oh, I was terrible. Really, really bad. Especially at geometry. When do you ever use that?

"I was good at English and history and art, and stuff like that. I was actually not bad at some science, but chemistry and calculus I was terrible at. I just couldn't process it. I was definitely better at the arts."

So was drama her big passion even then? "No. Smoking and drinking coffee were," she laughs.

At school Paltrow wanted to be an anthropologist, but her early fame - she wasn't even 20 when family friend Steven Spielberg gave her the role of Wendy in Hook - may have been the next best thing. Now she studies her notoriety and our primal reaction to it as if there might be a quiz later. "Sometimes people tell me that they read I was exorcising my house for a ghost, or I have a GPS satellite in my bag to watch my baby while she's sleeping. I think, 'Did you read this in a newspaper?' It's very strange," she says, creasing her brow again in pantomimed perplexity.

"To be honest, it makes me feel sad for the people who are coming up with it, because I think, karmically, it can't be very good for you. It depresses me to think of people trying to sell papers by dredging up bad things or bad news. It makes me feel sad for them. But then, I don't read it," she adds quickly.

"What I find really interesting," she continues, "is this strange kind of British thing of 'Why do you want to live in our country?' Your country's great - why wouldn't I want to live here? It's almost as if you don't understand why someone like me would want to live in your country."

Well, okay then, why does she? "Ha! Because my husband lives here and works here, and I find the whole psychology or the sociology to be really agreeable. I really like my friends here. They're really intelligent and really present, and they're not looking over your shoulder at dinner to see who's walking in. It's a nice place to live. It's not as hectic as New York, but you've got all the culture and more. It's not as vapid as LA, but you can still hop in your car and take your kid to a swimming lesson."

Like her friend Madonna, Paltrow has downshifted into a Cool Britannia lifestyle. Along with her vaguely blokey spouse, she relishes walks along the Serpentine, curry, warm beer and (unlike Madge) embracing our offerings on television. "If you'd told me five years ago that I would be watching re-runs of The Two Ronnies, I would have said you were clinically insane," she giggles.

Now, as she awaits the birth of 'the thing we cannot discuss', she is clear that her new schedule makes motherhood a priority. Between pregnancies she directed a short film and took small roles in the upcoming Running with Scissors and Love and Other Disasters. She has also just signed a contract as the face of Estée Lauder, but the workload does not appear onerous. In the pipeline there may be a film about Marlene Dietrich, but the script is still some way from being completed to her satisfaction, she says, waving away further enquiries.

By the end of the interview, Paltrow has thawed sufficiently to admit that, yes, Apple listens to and likes Coldplay, although when she was a baby her father's music operated largely as a soothing tranquilliser. More recently, her wilful toddler has been demanding repeat plays of Madonna's dancefloor hit 'Hung Up'. "Only she calls it 'So Slowly' by 'Dadonna'."

The desire for a life off-camera, her newfound contentment and, most of all, motherhood may combine to keep Paltrow out of movies for the foreseeable future, it seems. But the decision of a once fiercely driven actor to elbow Hollywood aside does not surprise Proof director Madden. "You always had to see Gwyneth and her family to make complete sense of her," he says. "That's who she is. She now has a family of her own, and I think that has completed her."

• Proof is released on February 24