The journalist used to the Gatwick Express and EasyJet, delivery into the lavish embrace of Prada is somewhat disconcerting. “I could get used to this,” you think, even as you worry that your shoes are all wrong, that your bag will fool no one, being neither new season nor vintage. At the 18th-century palazzo of the Fondazione Prada (its address is Ca’ Corner della Regina, though only rarely does anyone seem to use it) on the Grand Canal in Venice, no fewer than four black-suited young men are on hand to greet me: one to help me from water taxi to jetty, another to spirit away my luggage, and two merely to smile at me. “Please,” says a PR, leading me through the palazzo’s exquisite rooms (since 2011, these heavenly spaces have been used by the Fondazione Prada to display art). “Do go upstairs, where a buffet lunch will be served.” A buffet? Well, yes, the food is indeed arranged on a table. But when I approach a dish of gleaming asparagus – it’s so perfect, it might as well be by Manet – a waiter practically dives into my lap. If I’d like to sit down, he will bring me everything that I require.  It is the first week of the Venice Biennale. This lunch, doubtless one of dozens of similar gatherings around the city, is to celebrate the opening of Portable Classic, a new show at the palazzo which explores the miniature copies of classical sculptures that were such status symbols in later centuries. Needless to say, it’s a hot ticket. Who doesn’t want to be close to Miuccia Prada, an increasingly powerful figure in the art world?

Loitering, glass in hand, at one end of the room, I spot plenty of big names, Anish Kapoor and Carsten Höller among them – though it’s only when I clap eyes on Hans Ulrich Obrist, the itinerant and irredeemably well-connected curator and co-director of the Serpentine Gallery in London, that I know this is really the place to be. Obrist, of course, is already deep in conversation with our hostess, Mrs Prada – everyone calls her Mrs Prada, even those who have worked with her for decades – who slipped into the palazzo without fanfare a little earlier, and for a while I watch the two of them. While he is animated, arms windmilling wildly, Prada cuts an altogether quieter figure. Small and (unexpectedly) blond, she is wearing a white cotton dress with a pleated skirt. In her hand is a silk drawstring bag. In her ears are antique garnets or, more likely, rubies. On her feet are the kind of flat sandals, navy and white, that your granny wore at the seaside.

Two hours later, as the lunch is winding down and the diamonds and Chanel bags begin to exit the room, Prada approaches me and asks if I wouldn’t mind if we talked here, at one of the dining tables. It seems she has not yet had a chance to eat pudding and, sure enough, a waiter now puts in front of her a dish of panna cotta and roast peaches, an espresso (which she sends back, on the grounds that it is not hot enough) and some sugary biscuits. She eats quickly and greedily, and thanks to this, I warm to her – though it’s her face that really invites you in. Tanned as a nut, she wears no makeup, not even a slick of balm on her lips, while her expression is set somewhere between sombre and quizzical. It’s clear immediately that she couldn’t care less what I’m wearing; her eyes coolly meet mine, and never wander, not even to my (long-pondered and moderately daring) brooch. It’s as if she’s about to give me a tutorial. In her home city of Milan, the Fondazione Prada has just opened a vast “campus” for art on the site of an old distillery close to a railway line. I saw it the day before, and gasped at its size, its ambition, its severe industrial minimalism (even the children’s play area is grey and white). At 19,000 square metres, its collection of exhibition spaces – one is several storeys high and called the Haunted House, another is a grotto deep underground – is twice the size of Renzo Piano’s new Whitney museum in New York, and at least three times as elegant. Designed by the Dutch architect Rem Koolhaas, and filled mostly with work from the permanent collection of the Fondazione Prada, it has been received with some rapture by the critics, and with some gratitude by the Milanese, who will doubtless continue to make good use of its retro cafe – a 50s fantasy in green vinyl designed by the film director Wes Anderson – irrespective of whether they ultimately fall for the charms of Damien Hirst’s Lost Love (a gynaecologist’s chair in a large aquarium the artist made in 2000) or Nathalie Djurberg’s The Potato (a walk-in fibreglass tuber complete with purplish eyes that dates from 2008).

But is the woman who conceived it triumphant, over the moon, high on a combination of acclaim and relief? No, she is not. Only with the greatest reluctance, it seems, would Prada ever describe herself as pleased. “I’m always thinking about the next thing,” she says, her mouth turning down. “So I don’t enjoy anything.” But it’s so generous, her city of a gallery, with its square, its library, its cinema (visitors will be able to spend the day there for €10). She shrugs. “Well, I don’t feel generous. The result is maybe generous, but I didn’t start with that. I started with an idea, which was to do something that I think is important and relevant. I wanted to make culture attractive to the young [so that they would see] that it is necessary to your life. My intuition – and after many years, I realise that my main quality is intuition – was that it would be good to have a place where people could live with ideas.” Culture, she insists, must come to be perceived not as an extra, as a form of “decoration”, but as deeply useful. In what way useful? “It can answer political and even existential questions.”