Two years ago, Blue is the Warmest Colour, Abdellatif Kechiche’s explicit love story about the affair between two young French women, won the Palme d’Or. This year another film about a female same-sex relationship is set to follow in its footsteps. Todd Haynes’s Carol is an adaptation of Patricia Highsmith’s The Price of Salt, about the affair between a married mother and a shop assistant in early 1950s New York. It has met with a consensus of praise from critics in Cannes, with five star reviews across the board and talk of multiple Oscar nominations next year.

At a press conference for the film, Cate Blanchett was asked about an interview she gave last week to Variety, in which she appeared to come out as bisexual, saying she had had “many” past relationships with women.

Cate Blanchett and director Todd Haynes at the Carol press conference. Photograph: Yves Herman/Reuters

Blanchett, who is married with four children, said her quote had been judiciously edited for effect.

“From memory, the conversation ran: ‘Have you had relationships with women?’ And I said: ‘Yes, many times. Do you mean have I had sexual relationships with women? Then the answer is no.’ But that obviously didn’t make it.”

To laughter from the crowd, Blanchett continued: “But in 2015, the point should be: who cares? Call me old fashioned but I thought one’s job as an actor was not to present one’s boring, small, microscopic universe but to make a psychological connection to another character’s experiences. My own life is of no interest to anyone else. Or maybe it is. But I certainly have no interest in putting my own thoughts and opinions out there.”

Blanchett said she admired the restraint exhibited by the characters in the film, who speak about the sex lives only sparingly. “[Carol’s] sexuality is a private affair. What often happens these days is if your are homosexual you have to talk about it constantly, the only thing, before your work. We’re living in a deeply conservative time.”

Rooney Mara and Cate Blanchett in Carol

The actor confirmed that her research had involved consuming countless lesbian novels written in the middle of the last century, of which Carol appeared to be “the only one with a happy ending”. “They were outsider novels. Carol was not a card-carrying member of any sexual persuasion. That’s also important to remember: those labels, those groups, the comfort of them, didn’t exist then. The resultant isolation was very important.”

The film is the most mainstream American depiction of a lesbian relationship made to date. Its screenwriter, Phyllis Nagy, has spent 14 years attempting to get it made; that she finally had, she said, amounted to “a huge political statement.” In the time since Highsmith wrote the novel, “nothing has changed and everything has changed. Because we can have this movie now. It starts the kinds of discussion we need to have about this issue. We do not we politicise the material by just allowing people to live their lives honestly. [Gay people] are expected to make it an issue front and centre in our lives. But actually when you live your life, your identity is front and centre – but it’s something we’re not often treated to seeing in films.”

Phyllis Nagy, Rooney Mara, Todd Haynes, Cate Blanchett, Elizabeth Karlsen, Stephen Woolley and Christine Vachon at the Cannes photocall. Photograph: Loic Venance/AFP/Getty Images

The director, Todd Haynes, agreed that same-sex female relationships had been even less well-served by mainstream movie-makers than those between two men. The reason that the likes of Brokeback Mountain and Milk had preceded Carol was, he suspected, “because male audiences will not be excluded [by them]. They are the prime audience Hollywood are marketing films for.”

Rooney Mara at the Carol press conference. Photograph: Guillaume Horcajuelo/EPA

The cast and crew expressed the hope that the film might help change policy in the “70 countries round the world in which homosexuality is still illegal”. “It’s important to talk about,” continued Blanchett, while her co-star Rooney Mara, agreed “there’s a long way to go before we’re not talking about it”.

Blanchett also added her voice to the chorus criticising gender inequality at Cannes this year. The importance of female voices in film “fell off the agenda and we lost a lot of ground”, she said, before expressing her unhappiness at a recent headline declaring 2015 “the year of women”.

“You hope it’s not just a year. Not just some fashionable moment.”