A small woman seated with her hands on her knees, she almost goes unnoticed as she scrutinises the terrified model on whom busy hands are working. She dwells on the way the skirt falls, the top, the cream colours. Her hand indicates a change. The dress-maker, on his knees, adds a couple of stitches and moves back. "Like this, Madame Prada," he asks. No one moves. In the all-white workshop on Avenue Matignon, Paris, you could hear a pin drop.

Miuccia Prada, 63, is just like her collections: discreet, unpredictable and nonconformist. A brown turban holds back her fair hair. She wears old-fashioned earrings, a green crew-neck jumper, a brown, knee-length skirt, flat-heeled sandals and a brown leather bag. She is not beautiful but has a powerful presence. A remote woman and a fashion intellectual.

She currently stages her Paris shows at the Palais de Jéna, seat of the Economic, Social and Environmental Council. Apparently she likes the political ambiance, as well as the monumental colonnade and the view of the Eiffel tower. Some years ago she chose the headquarters of the French Communist party, an austere 1970s building designed by Oscar Niemeyer. "I always look for this sort of correspondence, for my ideas to take shape. This fantastic building, where we have beauty, surprises and political affinities, was just right for me," Prada says, with a piercing look that makes it clear she has no time for digressions. At home and abroad she gives few interviews, avoids social gatherings and shuns photographers.

Her mother ran a shop in Galleria Vittorio Emanuele II in Milan, selling luxury leather goods and accessories. Her grandfather started the business in 1913. Catholic and conservative, her family was typical of the Lombard bourgeoisie, but as a girl Prada soon realised she was different. In the 1960s she was the first person at her secondary school to adopt a hippy style. "I was conservative because of my parents, but when I was 14 I wanted to be different," she explains. "I had to be the first one to have an idea. The same obsession still drives me in my work, never doing things like the others. It's been a constant strand in my life."

Without working too hard she studied for a PhD in political science, then devoted rather more effort to learning mime at the Piccolo Teatro. To earn some cash she appeared in operas at La Scala and in TV adverts. "The theatre was a place where things were happening, where the avant-garde was taking shape. But of all that what I found strangest was mime," Prada says. Her parents' shop was the last of her concerns. Her world was the university, theatre and politics.

Joining the Communist party (PC) was not unusual for the children of Italy's middle-class. "In those days, if you weren't stupid, you wanted to change society and you were leftwing," she explains. "The PC was the 'soft' option. My friends were much more extremist and thought me conservative." She spoke at meetings campaigning for abortion but was bothered by the dress code. She liked skirts and was the only one in her clique never to wear jeans.

She loved politics and being involved in social issues, but retained her interest in appearances. "To want to be a fashion designer was really the worst thing that could happen to me. I thought it was dumb and conservative [...] But my education at home pulled the other way, giving me a taste for beautiful things, an instinct for fashion. I adored that."

Towards the end of the 1970s, Prada left politics and started working with her mother, designing bags. At a leather fair in 1978 she lost her temper with a Tuscan businessman who had copied her designs. But after thinking it over, she suggested a partnership. Patrizio Bertelli became her supplier, then her husband, the father of her two children and the brilliant business partner with whom she turned Prada into one of the world's leading luxury brands, backed by a firm operating in 70 countries.

She is the artist, he is the manager. For the past 34 years their volcanic exchanges have petrified staff, but together they have built an empire of garments, art and architecture, including a foundation that hosts top contemporary artists, produces films and organises conferences. Architect Rem Koolhaas has joined the game, stage-managing shows, designing shops and soon a huge contemporary art museum in Milan, in addition to the one in Venice.

"Fashion moves so fast," Prada says. "I work on waves which break really quickly. You can catch them, or you miss them in no time at all. Architecture stretches out over many years, giving me a sense of the long term which I need to understand the world."

• This article appeared in the Guardian Weekly, which incorporates material from Le Monde