WHEN your parents are an acting power couple, your uncle’s a Hollywood heart-throb and your grandparents also work in film, it’s understandable if you don’t think the movie business is that big a deal.

Maggie Gyllenhaal might have A-list pals and an Oscar nomination under her belt, but her seven-year-old daughter Ramona – whose father is the actor Peter Sarsgaard – isn’t at all dazzled by her mum’s day job. “I think she’s proud of me, you know?” says the actress, smiling.

“But I don’t think she thinks it’s the most amazing, glittering thing.”

Recalling some of Ramona’s observations, Gyllenhaal, whose brother is Brokeback Mountain star Jake, laughs, explaining: “It’s funny, sometimes she’ll say, ‘It’s hard to be an actress, you have to take your coat off, even if it’s really cold’.”

Despite growing up in Los Angeles, with her director father, Stephen, and screenwriter mother Naomi Foner, Gyllenhaal “never felt comfortable” there. At 17, she returned to New York, where she was born, to earn a BA from Columbia University (she also studied at London’s Royal Academy of Dramatic Art), and she and Sarsgaard now live in the city’s Brooklyn region with Ramona and her two-year old sister, Gloria Ray.

“My husband and I were both living in New York when we met, so we sort of just fell into living there,” says the 36-year-old, her voice croaking following a heavy cold.

Next on her wish list of places to live is London, where she filmed the upcoming BBC drama The Honourable Woman. “I feel like that’s really where I ought to be living. I just have to convince my husband.

“You know how in some cities you just feel like they welcome you in? I feel that way about London. You make friends easily and get the rhythm of the city.”

Gyllenhaal had her daughters in tow while filming the eight-part, BBC political thriller, her first TV role. She plays Anglo-Israeli Baroness Nessa Stein, who has inherited her late father’s arms business and changed the company’s purpose to laying data cables between Israel and the West Bank.

Nessa witnessed her father’s assassination as a child, was held hostage in Gaza as a young woman, and also harbours a dark secret from her past. The show’s topical political themes were part of what drew Gyllenhaal to the project: “In particular, the incredibly compassionate and thoughtful way those political ideas are dealt with.”

Mainly, however, she just loved her complex, powerful character. “She’s so much more alive than I am – than anyone is, really. It’s nice to be in her skin,” says Gyllenhaal, whose breakthrough role came in the controversial 2002 masochist fantasy Secretary, about a sexually dominant boss (played by James Spader) and his submissive secretary. The performance won Gyllenhaal a Golden Globe nomination.

Gyllenhaal, who also picked up an Oscar nomination for her role in the 2009 film Crazy Heart, carries off Nessa’s cut-glass accent with aplomb.

“I’ve done an English accent quite a few times now. I did it in Nanny McPhee Returns and in Hysteria. But this is the first time I’ve felt it was totally in my bones.”

When she and Sarsgaard aren’t working, they hang out with their daughters and try and go on the occasional run together (“He’s an ultra-marathoner, so he’s been getting me into running lately”).

She also sees plenty of her younger brother Jake when he’s in New York. “We are close.

And my mom really helps me with the kids, she’s been amazing that way.”

Career-wise, everything has changed for the star since becoming a mother.

“It just blew my heart open, and the spectrum of feeling got so much bigger on every side since I had kids. It definitely made me a better actress,” she says. “Also, there’s so much about planning. That kind of carefree, ‘Yeah, I’ll do that job, it’s all right’, it just can’t work like that any more. I have to really take my kids into account all the time.”

Being a busy mother also means Gyllenhaal, who will make her Broadway debut alongside Ewan McGregor in the Tom Stoppard comedy The Real Thing this October, doesn’t always have time to be camera-ready for paparazzi encounters.

“Lots of times I’m like, ‘OK, I’ve got the kids alone, I need to get Ramona to school, I just don’t have time for a sweep of mascara, I don’t have time for anything’.

“Sometimes I completely forget about it, and those are the times when I get paparazzied and I’m like, ‘Oh God, I really wish I’d put that cute hat on and sunglasses!’ “I can turn it out and make an effort when need to, but you don’t have to every day,” Gyllenhaal reasons. “Sometimes, you just have to put on jeans and a T-shirt, and take your kid to school.”

  • The Honourable Woman begins on BBC One on Thursday