The Guardian published online the interview and the photos from The Weekend insert.

I am half an hour early for the interview but the discreet hotel library has already been taken. A woman (blond, gangly, faintly familiar) is sitting on the floor, demolishing a plate of tenderstem broccoli. Pink-framed specs perch on the bridge of her nose. Her bare feet are tucked beneath the low coffee table. The woman looks up sheepishly when I slide open the door. She only crept in for a scavenge, she says. She can’t offer me broccoli because it is not hers to give. “Also,” she adds, “I’ve gone and eaten it all.”

The movie camera misleads. It can add voltage and glamour and a whole foot in height. And good actors transform, it’s the nature of the job. On screen, Blanchett has been an imperious Elizabeth I, a formidable Katharine Hepburn, a combustible “blue” Jasmine. In her latest film, Carol, she looms like a valkyrie over co-star Rooney Mara. I have been watching her for years and thought I knew just what to expect: some imposing snow queen, with wide geometric features and a hard feline stare. It is only now, gawping at the loose-limbed, studious-looking thief on the floor, that I realise I got it wrong. Blur your eyes and she might pass for Blanchett’s softer, sweeter, younger sister.

“Yes,” she says. “It’s me. Hello.” Then she plucks off her glasses like Clark Kent in a phone booth.

Blanchett is fresh off a night flight from New York, accompanied by Edith, her 10-month-old daughter, who didn’t sleep a wink the whole way. She’s hungry and knackered. She turned 46 last May, and jokes that she doesn’t spring back like she used to. “And actress years are like dog years. So that makes me about 120.” Not so long ago she feared that her film career might be done. If anything, it appears to be picking up speed.

Blanchett is in London to attend two movie premieres. In the first, Truth, she stars as Mary Mapes, the CBS journalist who found herself targeted by the Bush administration during the fraught run-up to the 2004 election. In the second, the extraordinary Carol, she plays the sculpted 50s housewife who sets out to seduce a Manhattan shopgirl. She’s great in both, although Carol has the edge for me, in that it contains more depth, more nuance, more giddying extremes of cold and heat. This quiet storm of a film is adapted from a Patricia Highsmith novel so nakedly autobiographical that the author felt she could publish it only pseudonymously. It is gracefully directed by Todd Haynes, who made his name at the vanguard of the New Queer Cinema movement and seems drawn to tales of transgression and tragedy (Far From Heaven, Safe). Blanchett reckons nobody else could have made it.

The pair last collaborated on the 2007 film I’m Not There, a fractured, skittish Bob Dylan biopic in which six actors were cast as the mercurial singer. Blanchett cropped up as androgynous Bob, decked out in black, a cigarette on the go, whereas tragic Carol Aird, the eponymous heroine of the new film, could hardly be more feminine. She’s an explosion of platinum hair and crimson nail polish, a dry martini parked beside one fur-coated elbow. Virginal Therese (Rooney Mara) is knocked for six and falls in love – and Carol appears to love her back. Except that this is Eisenhower-era America and Carol is married, so the pair’s only hope seems to be a life on the run. The lovers’ equivalent of Brokeback Mountain turns out to be a cheap motel in Waterloo, Iowa; the Christmas snow heaped up outside and a suspicious salesman in the room next door.

I plop myself on an armchair but this perch feels all wrong. I’m looming over Blanchett just as she did over Mara. If she can lounge on the rug, I guess I can as well. It’s informal; it’s convivial. We might be hanging out at some student party.

“À la Japonais,” Blanchett says with a grin. “I always prefer sitting on the floor.”

The broccoli all eaten, she pours us some iced water, every inch the efficient, confident host, though she still has her guard gently raised. She explains that she was drawn to Carol (the film) because of its thick shadows and secrets, its air of pungent melancholia. And she was drawn to Carol (the character) because she is flawed and fragile; it’s as if she comes alive only in the wings. “It’s not just their gender that’s keeping Carol and Therese apart,” she explains. “It’s the class difference. It’s their age gap. But, yes, her sexuality has effectively made her a criminal and Carol knows the cost of acting impulsively. She has to plot each liaison as if she’s plotting a crime.”

Carol is set in the bad old 1950s. But I wonder whether there remains a taboo in depicting same-sex relationships in mainstream US cinema.

Blanchett shrugs. “Well, the fact that we’re talking about it means there are still barriers. It’s like the situation with women in film – or, frankly, women in every industry – not being paid the same as men. You have to keep it on the agenda. You have to keep it politicised. But I’m not very interested in agitprop cinema. That’s the realm of the documentary. That’s where investigative journalism belongs. The problem is that when you represent a character in a same-sex relationship, it’s like you have to represent them all. You become a spokesperson, which really isn’t the point. When the time comes that we have a diversity of same-sex couples in film, then the problem is solved, I don’t have to stand for everyone.”

Her recent experiences at the Cannes film festival provide a case in point. Following Carol’s press showing, Blanchett told a Variety reporter that she had personally had many relationships with women – which was technically true, in that she has friends and family and colleagues. But the resulting story went viral, and eclipsed the movie itself.

“Look,” she says, rolling her eyes at the memory, “I also just played Mary Mapes, who’s a journalist. No one asked me how long I’d been to journalism school. If I played someone who has an affair, I think a reporter would probably think twice before asking, ‘Ooh, how many affairs have you had?’ It would be a slightly delicate area. But there are no holds barred about asking me whether I’ve had relationships with women. And so I facetiously said, ‘Oh yes, I’ve had many relationships with women’ – because frankly, who hasn’t? Of course I said it in inverted commas. But the inverted commas didn’t make the page.”

Perhaps the confusion stems from our garbled interaction with actors, I suggest. We see a face on the screen and assume we know them. Blanchett nods; she understands what I mean. Film can be a weirdly intimate medium. “I used to think it was more profoundly felt in TV, because you’re in someone’s home, performing for them in their living room. But now film comes in just as close. People will probably watch Carol on their mobile phone. I’m probably going to be in someone’s pocket. Which is deeply intimate. I don’t even want to think about that.”

She pauses. Another memory has surfaced. “It was the same for me with Alan Alda in M*A*S*H. My father died when I was young. And Alan Alda looked just like my father. And I would watch it five days a week, just to imbibe him and say hello. So when I eventually met him, my God, he must have thought I was some sort of mad person. I ran up to him as though I was seeing my dad.”

Robert DeWitt Blanchett was a petty officer turned ad man, originally from Texas; his wife a teacher and later property developer. The family (mum, dad, three kids) lived a comfortable existence in the suburbs of Melbourne. When Blanchett was 10, her father left for work one morning, waving her goodbye through the window as he passed. Later that day he suffered a heart attack and was gone. Her grandmother would later move in to help with the crisis and the family endured; they clung to one another. “But yes,” she says lightly. “That was a pretty dark time.”

I’m interested in how she then found an escape into acting. Sources state that she made a low-rent film debut while she was still in her teens, playing a cheerleader in an Egyptian boxing movie called Crabs. Except it transpires that the sources are wrong. Yes, she says, she was living in Egypt on a gap year abroad, because at the time she was planning on becoming a museum curator. “So I was in this fleapit in Cairo, which has probably long since burned down, called the Oxford hotel. They printed passports and money in the foyer. And this random Scottish guy came up and said they were looking for English-speaking extras, and that I’d get paid five Egyptian pounds and a falafel. At the time I didn’t have enough money to pay my room for the week. I went along and there was an Arabic guy with a megaphone, like something out of a silent movie, and it was so hot and so boring that I left.”

So she was never in the boxing movie? “Nooo,” she groans, like a teacher correcting a particularly dense student. “But you can say that I was if you want. Print the legend of the boxing movie.”

Back in Australia, she enrolled at drama school and decided she might as well give acting a shot. I tell her she makes herself sound rather passive and again she corrects me; it was not like that at all. “Acting had become like this terrible addiction. I felt I needed to give it five years and see where it took me.”

Specifically it took her to the Sydney stage, through acclaimed turns in Sophocles’ Electra (while she was still a student) and David Mamet’s Oleanna (shortly after graduation). It carried her to a Bafta award for her breakthrough role in the 1998 film Elizabeth. “I was shocked,” she recalls. “You know, I called my agent after making Elizabeth and said, ‘I think I’ve ended my career before it’s even begun.’ So yeah, I was completely shocked by how that film was received.”

Since then, it all looks to have been plain sailing: a canny blend of multiplex blockbusters with classy human dramas; an Oscar for her pitch-perfect impression of Katharine Hepburn in Martin Scorsese’s The Aviator. She points out that she once made a comedy – Bandits, co-starring Bruce Willis – that had the misfortune to open the same week as the 9/11 terrorist attacks and promptly sank without trace. But in scanning her credits, there aren’t many obvious duds. Her career has been positively serene.

“Serene?” She guffaws. “Harmless, that’s what you’re saying. You’ve had an absolutely benign, innocuous career. Congratulations!”

In her mid-20s, she met the Australian playwright Andrew Upton. They bonded over a late-night poker game; he proposed marriage just weeks later. They now have three sons (Dashiell, Roman, Ignatius), along with baby Edith, whom they adopted in March. Blanchett reckons the children keep her honest. “They force you to be economical. To choose your roles wisely and then shrug them off as soon as you’re done.” She says people always ask how she is able to juggle her roles as an actor and parent. “Now, I might be wrong, but I don’t think they put the same question to male actors, do they?”

Her career was still in its infancy when she married Upton. How would he say she has changed in the intervening two decades? “Umm.” She screws up her face. “I think he would say I’ve got better at my job. That I’ve learned to get out of my own way a bit more. I think perhaps he would say I’m a little less socially awkward. I hope so anyway. I used to be very socially awkward. Walk into a room. Not know what to say.”

In 2008 she took the decision to limit her film roles in order to join her husband as co-artistic directors of the Sydney theatre company. She knows the move was a gamble; it risked closing the door at her back. “When I stepped away to run the theatre company, a lot of people said, ‘This is a mistake. You realise you have a certain shelf life and you’re throwing that away.’ But I think it’s made me a better actor. If it hasn’t, I’m a fucking idiot.”

She pauses. “But you do carry that fear with you. When I was getting ready to leave [the company], I did think, ‘Well, I’m in my 40s, I don’t know if I’ve even got a film career to go back to.’ And then Blue Jasmine landed in my lap.”

Her role as Jasmine Francis, the brittle Park Avenue princess fallen on hard times, would go on to win Blanchett a second Oscar. But the experience of shooting it was no bed of roses. She describes Woody Allen’s directing style as one of “benign neglect”, although it doesn’t sound altogether benign to me. “The first day was brutal,” she recalls. “He came up to me and said, ‘This is awful and you’re awful.’ As if he were talking about someone else, some other actress, and that maybe I could go and have a word with her. And then three weeks later it turned out that he didn’t like the costumes, he didn’t like the locations, he didn’t like the scene. He said, ‘You’ve got to help me rescue this movie.’”

The trick, she decided, was to take charge of the situation; to bombard the director with questions. “I realised I had to demand things from him. And sometimes he would look at me just bewildered. But I’m not particularly needy. A lot of times, actors ask questions and what they’re really asking is, ‘Was I good? Did you like me?’ But my questions were all technical. ‘Should I stand here? Should I say it that way?’ And he would answer my questions maybe half of the time.”

What about the other half? “The other half he didn’t hear me.” She laughs. “Or he was pretending not to hear me.”

She sat down to watch the finished film in a funk. She didn’t know what she’d done. She didn’t know how it would turn out. “Oh, it was brutal, I was sweating bricks. Is that right? You don’t sweat bricks.”

Sweating bullets? “That’s it. You shit bricks and sweat bullets. What a great phrase. Sweating bullets.”

So what was the verdict? Did she think it was OK? “Yes,” she says, but as if the question alarms her. “I mean, there are always bits that I wince at. I always have to prepare myself. Seeing yourself on screen is excruciating.”

Blue Jasmine was a gift. Those films don’t come along too often. All the same, she feels that most characters present at least some form of challenge. “Acting can be an anthropological process,” she says. “I don’t want to sound wanky or pompous about it – my son calls it pump-ass – but I think that’s what it is.” She is fascinated by the tension between how people project themselves in public and who they become behind closed doors; their capacity for surprising themselves most of all. Surely there have been occasions when a character has defeated her, when there are simply no hidden depths to explore? How about Galadriel, the distant, dreary elf queen from The Lord Of The Rings? The actor snorts; she’s not about to disown Galadriel. “Pointy ears,” she says. “What’s not to like?”

Even Galadriel’s not perfect, everybody has their flaws. “You know that eastern idea of perfection? The idea that something can be truly perfect only if there’s an imperfection in it. We all have that, it’s what makes us human. And it doesn’t matter if you’re playing Elizabeth I or Bob Dylan or Mary Mapes or Carol. You’ve got to find as many warts as you can.”

Is it important for her to have some affection for the people she plays? “No, I don’t think so. But I think that empathy is a noble cause. I think a point of understanding is probably a good thing. I mean, with some people it’s harder than with others. If I was playing Donald Trump, it might be a tall order.”

I tell her I’d like to see her play Donald Trump and she hoots with laughter. “I would play Donald Trump in a heartbeat,” she cries. “The comb-over? I’m there. Todd Haynes could make a whole new film. Six different incarnations of Trump.”

Her diary is full for her three days in London. She has tickets to see her old friend Nicole Kidman on stage in Anna Ziegler’s Photograph 51. She has another friend who is about to open in a production of La Bohème at the ENO. She really wants to see Imelda Staunton in Gypsy; she would quite like to see the Suffragette film, too. Blanchett points out that she and Upton lived in Brighton for nine years, around the turn of the century, which makes any visit to the UK a homecoming of sorts. But when I ask where the family is based at the moment, she turns oddly cagey. It’s as though she thinks I have become rather too comfortable sitting with her on the floor. Well, the boys are all at school in Sydney, she explains, so that probably means that Sydney remains home. But right now the family is drifting, they have no particular ties.

Seemingly apropos of nothing, she recalls a job she took, straight out of drama school, when she worked as a script reader for a casting agent. The job provided her with the ideal vantage point, the perfect training for her fledgling career. She would sit quietly in the corner and watch the actors walk in and walk out. Some of them were dead the moment they pushed open the door. Too tall or too short. Too blond, too brunette. Then there were the others who ran at the audition too hard. Those were the ones who she really felt for. They wanted it so much and could not conceal the desire, and they tripped and stumbled on their own nervous energy. She says, “And at some point I realised: that is the act. It’s not whether you can act or not. It’s whether you can act comfortable and relaxed.”

She gestures down at herself: exhibit A on the floor. “I’m not comfortable,” she says. “I’m not relaxed. It’s all down to acting.”