“I don’t feel like I’m a very composed person,” says Cynthia Nixon. Right now, that’s rather hard to believe. The actress, famed for her role as the red-haired Miranda in Sex and the City, is barefoot, curled up on an armchair and shrouded underneath a blanket in a white-walled London hotel room. On the table in front of us is a white tea set. Her hair back to its natural blonde, she couldn’t look more composed if she tried.

Nixon clarifies. Raised in New York – her mother was an actress, her father a radio journalist – she says her parents brought her up “in a natural way with not a lot of emphasis on appearances”. Very un-Miranda, you might say. “There was never a lot of focus on...you really should go brush your hair! Not composed in that way. There’s not a lot of difference between me in private and me in public, I suppose that’s what I’m trying to say.”

Indeed, the 50-year-old Nixon is not one for hiding her real self away. She had two children with her college sweetheart photographer Danny Mozes – Samantha, now 20, and Charles, 14. After they split, she began dating education activist Christine Marinoni. “I’d never fallen in love with a woman. But when I did, it didn’t seem so strange,” Nixon said back in 2007. Marinoni later give birth to a son, Max, in 2011, and the couple married a year later.

Actress Nixon was chosen to play Emily Dickinson by the film's director/writer Terence Davies because she had an affinity with the poems and he thought she looked like her (AP)

On the surface, at least, she couldn’t seem further from her latest character, 19th century poet Emily Dickinson, whom she plays in the new biopic A Quiet Passion. You might call it the role of a lifetime. It’s “definitely, absolutely” the most challenging part she’s played, with Nixon steering the character from her collegiate years to her painful death from kidney failure in 1886, by which point just a handful of her poems had been published.

The challenge, says Nixon, came in “depicting someone who, at times, is so full of love and excitement about the world, but also has such deep emotional and physical pain”. Not to mention the difficulty of externalising the inner demons of this Massachusetts spinster – an increasingly reclusive, secluded figure in her later years who, at least after her death, became known for such melancholic works as “Because I could not stop for Death”.

“I think she’s an extraordinary person,” says Nixon. “I think whatever she would’ve done, whatever field and era she would’ve found herself in, she would’ve succeeded. And maybe she would’ve lived now and been very solitary. I do think she would’ve found an audience more readily had she lived now…I think she would be astonished to see how not just famous she is, but how important she is to other writers and to readers all over the world.”

Nixon (right) with (from left) Willie Garson, Sarah Jessica Parker, Kristian Davis and Kim Cattrall in the third season of HBO comedy ‘Sex and the City’ (Getty Images)

With the film co-starring Jennifer Ehle as Dickinson’s sister Vinnie, for Nixon the poems weren’t so alien. She grew up in a literary household, with Dickinson a presence. “We had a record of some of her poems and letters read by Julie Harris [the actress famed for starring in the one-woman play about Dickinson, The Belle of Amherst],” she explains. “So from a very early age I was exposed to it – and orally, and not just on the page.”

Her knowledge was immediately apparent when she met Terence Davies, the British writer-director behind A Quiet Passion. We were talking about Emily Dickinson,” he recalls. “When her [Nixon’s] mother died, she said a poem of hers ran through her mind. I thought, ‘She knows the poetry and she looks like her!’” He immediately asked her to join the project.

Nixon even admits an affinity with the poet. “I do feel I have a lot of Emily qualities,” she says. “I’m not so shy anymore but when I was young, I was very shy. I feel like I presented myself in an Emily way – I’m very, very interesting, if you would just take the trouble to get to know me; you would find me really fascinating, but I can’t get out in the market place and sell myself!”

Nixon as poet Emily Dickinson (left) and Jennifer Ehle as Dickinson’s sister Vinnie

It seems a strange statement given Nixon was 12 when she started acting. By 1980, in her early teens, she’d her feature debut with Tatum O’Neal in Little Darlings and her Broadway bow in a revival of The Philadelphia Story. There were early roles in Milos Foreman’s Mozart drama Amadeus and two appearances for Robert Altman – in his teen comedy OC & Stiggs and his political mockumentary Tanner ’88.

She carried on quietly through the 1990s – popping up in films like The Pelican Brief and Addams Family Values – although motherhood took precedence. What did it teach her? “It teaches you to be firm. It teaches you to be forgiving. But I also think, one of the things, particularly as your kids start to get older, it teaches you that as much as you want to do everything you can for them, you need to take care of yourself.”

It wasn’t until 1998 that Sex and the City arrived, becoming a phenomenon almost immediately. “It completely changed my life,” she admits. “I’d been acting almost 20 years at that point. And I’d had a lot of success, but nothing like that. It’s extraordinary still. Even if I get older, even if my hair is a different colour, even if I’m in a place that people don’t expect me to be, heads are always turning.”

Nixon then adds a postscript: “Eventually one day they won’t.” But that’s hard to figure. Even after the show finished in 2004, her career has remained intriguing – from playing Nancy Reagan in the recent TV movie Killing Reagan to a cancer sufferer in indie James White (Nixon’s mother died of cancer and she herself received treatment for early stages of breast cancer a few years back).

Recent rumours have suggested a third Sex and the City movie (the first two grossed more than $700m [£560m] between them) is in the offing. “Y’know, I’d be delighted. I don’t think it’s time [has passed],” she says, when I ask how she’d feel about reuniting with Sarah Jessica Parker et al. Of course, since the last movie – in 2010 – Lena Dunham’s TV show Girls has rather usurped it.

Nixon admits she’s a fan of Dunham’s show, which is currently in its final season. “I think it’s fantastic. It’s so creative. It’s so true. And it’s so dark. I think that’s one of the good, smart things Sex and the City did. It wasn’t just jingoistic – women are great, we’re unstoppable! That gets tiring after five minutes.” She fixes her eyes on me. “Women are endlessly fascinating and deeply fucked up, right?”