Prada’s profits fell 25% in the first half of this year, while the status of Miuccia Prada as Italian fashion’s go-to intellectual finds itself under threat from Gucci’s newfound enthusiasm for “allegorical cartography and rhizomatic thinking”. (Me neither.)

But this Milan fashion week catwalk show – a film-meets-fashion showcase in collaboration with David O Russell, director of American Hustle and The Fighter – was a strong statement that Prada is not content to be yesterday’s brand. 

Prada, which this summer became one of the very last luxury brands to enter e-commerce, is embracing modernity. After a series of collections in which Prada has sought to unpick femininity’s backstory in relation to contemporary fashion – the role of lace at formative moments in women’s lives, for instance – she said backstage after this show that she was finished with her “historical period”.

“Enough with talking about the past, about what women have carried on their shoulders all these years,” she said. “It is time now to talk about the present.”

The notion of a woman in the spotlight and in jeopardy – the Miuccia role, arguably – was played out in Russell’s film, projected above the metal mesh catwalk throughout. It showed the actor Alison Williams in a blond Marilyn Monroe wig being followed through an airport, and watched by a long lens photographer.

The clothes on the catwalk, too, had a sense of intimacy. These were not show-pony catwalk classics but clothes a woman might wear to go about her day, unaware of being observed.

Their hair combed flat and secured with kirby grips, their heels sensibly low and their skirts a non-fashion knee-length, the models seemed to parody everyday dressing. But this being Prada, there were twists: brown and green, colours most women shy away from in real life, pervaded the catwalk, while a simple trench coat featured maribou feathers at the cuff. 

For fashion consumers of a certain vintage, the name Max Mara will always conjure up a camel coat. But for teens and twentysomethings, Max Mara is now most closely associated with the image of model of the moment, Gigi Hadid. Hadid opened and closed the Max Mara show, her first catwalk appearance in Milan, and was joined by her model sister Bella. The night before the show, the Max Mara flagship store in the city was mobbed by fans who gathered for a glimpse of Gigi Hadid at the launch of the BoBag handbag.

The attention on Hadid took an unpleasant turn after the Max Mara show, when Ukrainian prankster Vitalii Sediuk, previously arrested in LA for a red-carpet scuffle in which he broke Brad Pitt’s glasses, seized the 21-year-old as she walked to her car, lifting her off the ground. Hadid freed herself by elbowing her assailant, and had to be held back by a security guard from pursuing him. Hadid later hit back at news reports which focused on her actions rather than Sediuk’s, tweeting that she “had EVERY RIGHT to defend myself. How dare that idiot think he has a right to man-handle a complete stranger.” Alluding to his retreat in the face of her vigorous self-defence, she signed off “he ran quick tho”.

On the catwalk, however, all was serenity. The camel coat was nowhere to be seen on the catwalk, this being a spring collection. Instead, lush green palm prints and sultry pencil skirts, worn wriggled high onto the torso and belted tightly at the waist, starred in a homage to Lina Bo Bardi, the Italian-born modernist architect whose long career in Brazil included the design of São Paulo Museum of Art. The contrast of slick, hard-edged silhouettes and fauna-splashed prints was inspired by Bardi’s quasi-brutalist buildings in their lush Brazilian context. The pencil skirts and bright colours came from the Tropicalia countercultural movement of 1960s Brazil, which Bardi was associated with, and which drew on the iconography of Brazilian folk heroine Carmen Miranda. 

This concept of bombshell glamour with intellectual chops runs through every collection which British designer Ian Griffiths creates for Max Mara. The first campaign for which Max Mara recruited Gigi Hadid in 2015 was based on Eve Arnold’s photographs of Marilyn Monroe reading Ulysses; other recent seasons have been inspired by Dorothy Parker, and by the Russian artist Lyubov Popova. 

The look – dubbed “voluptuous modernity” on the programme notes – was accessorised with bucket-shaped handbags, a style which looks to be holding strong into 2016, and by high-heeled, perforated clogs that which resembled Crocs, stoking speculation that the plastic shoes, which starred in Christopher Kane’s London Fashion Week show, will be next summer’s cult footwear.The look - dubbed “voluptuous modernity” on the programme notes - was accessorised with bucket-shaped handbags, a style which looks to be holding strong into 2016, and by high-heeled, perforated clogs which resembled Crocs, stoking speculation that the plastic shoes, which starred in Christopher Kane’s London Fashion Week show, will be next summer’s cult footwear.