In an hotel in Amsterdam, the Labèque sisters, the finest and chicest piano duo performing in the world, want to talk about shoes.

Katia and Marielle — the stars of the Proms this year, with appearances in three concerts — think about clothes in a way that few else do in classical music. It’s all Dior tops and skinny jeans for these two. I’m concerned for them, however. Will they be able to match their fellow opening-night performer Stephen Hough, whose footwear is also normally pretty darn snazzy? Can they beat, say, his green velvet slippers? “Well,” Katia rejoins, “I’m wearing Louboutin.” That means 5in heels and bold red soles. Touché.

There is a good chance that there will be a touch of style in the audience, too, from the sisters’ stellar chums — Sting or Madonna, perhaps, even Herbie Hancock’s nimble fingers digging into an interval ice cream.

The sisters have over the past 30 years crisscrossed the worlds of jazz, pop and classical, picking up a list of mates that reads like a Grammy award ceremony. Chick Corea, John McLaughlin (Katia and he were an item), the late Miles Davis, Ira Gershwin and Olivier Messiaen. Davis, a regular in the audience, was even inspired to write the song Katia, “which was great”.

It’s not hard to see why they win friends. Their quiet barrage of prettiness, warmth and impishness is pretty irresistible. And in conversation, as in their piano playing, they seem to complement each other. Katia takes the extrovert treble line of engagement, hardly pausing for breath, while Marielle pads along behind, otherworldly, often starting or finishing sentences with a whimsical Gallic rumble.

Later at the Concertgebouw they are to play a Louis Andriessen piece, The Hague Hacking, which will receive its British premiere at the Proms on August 17. In the green room they mooch about like rock chicks. In fact their British debut  was at the Roundhouse, performing Boulez’s complex Structures, sweating it out in jeans and T-shirts with the composer conducting.

For their New York debut they performed Messiaen and Stravinsky in the first half, before Katia joined McLaughlin, on guitar, for a second-half jam. One rocker ran up to Katia, desperate to know what the Labèques had played. “Stravinsky,” she’d said. “That guy’s great!” he exclaimed, “Does he have a band?”

Their careers started conventionally enough in Paris in the Fifties. Their mother, a pianist who had been taught by Marguerite Long, tried to persuade the girls to play together when Marielle was 6 and Katia 8. The partnership lasted barely a few minutes as they ended up pushing each other off the chair fighting for control of the pedals. Through their teenage years and the Paris Conservatoire they studied as soloists. Only after they graduated did they give duetting another crack, this time with a piano each.

They dived into the deep end with tough contemporary repertoire such as Messiaen’s Vision de l’amen. One day while they were practising the work Messiaen, who was a professor at the Conservatoire, overheard them and suggested that they record the piece. An extraordinary first album put them firmly on the critical map. They started to work with contemporary composers but then an album of Gershwin’s Rhapsody in Blue sold half a million copies and catapulted them to fame.

With success in the classical realm secured, Katia started experimenting around the edges. She dated McLaughlin — “I always date guitarists” — moved to Monte Carlo and fell in with some jazz greats: Corea, Davis and Hancock.

Today they flit seamlessly between Waldbühne in Berlin and the post-rock scene at music festivals such as All Tomorrow’s Parties. They have worked with Sting and played for Madonna. Katia says that the pop star loves her Satie and Ravel. “She knows a lot about classical music.”

All of this cross-pollination feeds into their pianism. The intense improvisatory quality of their playing is born of these experimental ventures. Whether Mozart or Stravinsky, their musical line always sounds as if it is being woven for the first time. Even the new Andriessen piece was unravelled like a riff, Katia head-banging her way through the Dutch performance. Yet the concerto has been one of the hardest they have had to learn, they say: six months to master 16 minutes of music. And there’s no let-off, Katia explains: “You can’t abandon it for one day.”

But some romantic pieces, staples of the duo repertoire, they don’t even rehearse. “And I hate scales,” Katia says, shaking her head. She prefers to work runs out within the context of a piece.

When Dirk Bogarde was a neighbour in London, they tell me, he infuriated the pair by sending them a letter about their “scales”. “We were so excited,” Katia explains. “He must want to meet us, we thought. Instead, the letter said how much he hated our music and the constant scales! I’ve never done scales in my life!” she exclaims. She was preparing Mendelssohn’s double piano concerto, which has a lot of arpeggio runs — “not scales”. Bogarde later tried to kick the door down, Katia claims.

For her current guests in her house in Rome, the Andriessen piece apparently sounds like a piano tuner at work. The confusion is understandable. The piece works essentially like a game of tennis, notes flying from Katia to Marielle and back, a medieval musical technique called hocketing. The sonic effect is a thrill. “He has managed, somehow, to create a completely new concerto,” Katia says.

Expanding their repertory is a hugely important task because, to be frank, there’s not much out there. Many composers don’t like writing for the combination. “One piano is enough, they say,” Marielle says, laughing stoically. “And sometimes it’s true.”

What makes a good two-piano piece work above all else is dialogue. And the same is true of a good performance. “When people say, ‘It was so great, you sounded like one’, we don’t find that necessarily complimentary,” Katia says. “We like to sound like two different voices!” The trick, they say, is to learn how not to play together; how to bend around each other like singers do with their backing musicians.

With their pianism so special, why don’t they play some solo performances? “I would feel lonely,” Marielle says, smiling shyly. Katia does sometimes contemplate this. But then she sticks on a CD by the Polish pianist Krystian Zimerman, “and I feel fine again”, she says. “Anyway,” she adds, letting out a huge Gallic puff, “it’s so much less work!”

Igor Toronyi-Lalic