The red carpet at the Cannes film festival is an elysium of old-fashioned glitz and glamour, but the festival faced controversy on Tuesday after it emerged that it takes the odd bout of tyrannical fashion policing to keep it that way.

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A group of women in their 50s were turned away from the gala screening of Todd Haynes’s Carol for allegedly not wearing high-heeled shoes, according to industry newspaper Screen Daily. The women, some of whom had medical conditions, were apparently barred entry for wearing rhinestone flats.

The festival is facing a backlash from film fans protesting against what many perceive as a sexist dress-code policy, even though Cannes’s director, Thierry Frémaux, has denied that high heels are obligatory. “The rumour saying the festival insists on high heels for women on the red carpet is unfounded,” he said in response to critics on Twitter.

Among those joining the backlash was actor Emily Blunt, who was due to walk the red carpet on Tuesday night in support of her new film, the FBI drama Sicario.

Facebook Twitter Pinterest Rachel Weisz at the premiere of The Lobster. Photograph: George Pimentel/WireImage

“Everyone should wear flats, to be honest. We shouldn’t wear high heels,” said Blunt, when asked about the controversy at the Sicario press conference. “That’s very disappointing, just when you kind of think there are these new waves of equality.”

Sicario director Denis Villeneuve joked that he and Blunt’s co-stars, Benicio del Toro and Josh Brolin, would wear high heels to the premiere in solidarity. Del Toro then mimed wobbling along the red carpet from his seat. However, Villeneuve and his actors wore men’s shoes when they appeared on the red carpet before the early evening premiere.

Also critical of the dress code was Asif Kapadia, director of the Amy Winehouse documentary, Amy, which premiered in Cannes last week. Kapadia tweeted that his wife had initially been denied entry to the screening because of her footwear, but was eventually allowed in.

asifkapadia (@asifkapadia) @muirkate happened to my wife (eventually let in)

It has also been reported that a film producer who has had part of her left foot amputated has also been stopped for not wearing high heel shoes. Valeria Richter told the Telegraph she had been reprimanded on the red carpet for her footwear, despite missing her big toe and part of her foot. She said she had been stopped four times by officials at the premiere for The Sea of Trees, but had eventually been allowed to proceed. Richter said: “We put on the dress and make an effort to be formal and festive, but to demand heels is not right.”

Cannes’s red-carpet screenings are by invitation only. The official dress code is explained to guests after they collect a ticket for their film. Published guidelines are hard to come by, but it is generally understood that men must wear black tie with black shoes and women must be elegantly dressed with smart footwear. Festival staff questioned by the Guardian seemed unclear as to whether high heels are obligatory at red-carpet screenings or not.

Gender equality has been a key theme in many of the films in year’s festival selection. Ironically, Carol, the film to which the flat-wearing guests were allegedly denied entry, is perhaps the film in competition at Cannes with the strongest feminist message. Based on the book by Patricia Highsmith (herself an avid fan of loafers), it tells the story of a young shop assistant, played by Rooney Mara, who embarks on an affair with a married older woman.

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Outside the Palais, 20-year-old Tami was one of many film fans hopeful of being given a spare ticket to the Tuesday-night premiere by a charitable delegate. She was carrying her high heels in a plastic bag.

“It says on your ticket that you have to be smartly dressed,” she said. “For women that means high heels. I wish we didn’t have to. They’re uncomfortable.”