At home with the dress designer who counts Victoria Beckham and the Duchess of Cambridge as fans

Fashion designer Jane Lewis is recalling the moment she and her husband, Peter, found their house over 20 years ago. 'I think a house chooses you,' she says. 'It didn't look anything like it does now, but as soon as I stepped through the door I just knew it would be home, in the truest sense of the word.'

It is a house that many people would wish to be chosen by: a beautiful Georgian property overlooking a leafy square in Bayswater, with a first floor that extends laterally across three buildings. "It wasn't a particularly nice area at the time," Lewis points out. "It's really changed. You hear about areas regenerating, but we've lived through it."

After starting out as an assistant to the designer Elspeth Gibson, Lewis launched her own fashion label, Goat - named after the cashmere that was the mainstay of its first collections - in 2001, at the age of 26.

Its signature is luxurious but wearable clothes that can be worn from desk to dinner, and its bestselling shifts and tunic dresses have garnered high-profile fans including Victoria Beckham, Samantha Cameron and the Duchess of Cambridge.

In March, Lewis branched out with Kid by Goat, which translates the aesthetic into simple but stylish dresses for children. "It's been a long-time wish of mine," she says of the line.

"I bought the name years ago: it was just so perfect. I was looking for a dress for my daughter and found myself in a style void. I wanted to create that timeless, pure look of old-style Dior childrenswear, or pictures of Jackie Kennedy with her children: not prissy, just a very clean, simple silhouette. We've applied the handwriting of Goat and literally made it mini."

At £180 each, the dresses are at the high end of the market, but Lewis believes that children should look like children, and she applies that approach to her family's home life, too.

Their house is undoubtedly grand, but no part of it is out of bounds to Ines, 13, Bay, 10, and Rex, seven. "They do their homework in here, make videos, build dens," she says of the formal dining room with its Venetian chandelier, enormous bespoke table and old masters lining the walls.

The interiors are painted throughout in bright white - "just an arctic white by Dulux, nothing snazzy" - which is redone every five years or so: quite a production, requiring scaffolding. Yet she tries to remain calm when a greasy fingerprint appears on a wall a few days later.

"There's nothing I can do about that, it's just life," she says. "They have to be allowed to be children; it's not their fault the house is white. I don't want them to grow up in a place where they're not allowed to touch this or use that."

What really made the place a family home, however, was their renovation of the basement 10 years ago. It's now a fresh, bright space with a kitchen, a dining table and a sitting area that opens on to the garden.

"We made this a much bigger space as our family expanded," says Lewis. "We've grown up in this house, adapted it to our needs. This is a proper family room - it's been knocked, played in, banged about."

It's also a good example of her flair for juxtaposing old and new, the sleek Bulthaup kitchen teamed with an antique mirror, old paintings, and her favourite recent acquisition: a black 1950s Swedish chest bought from antique dealer Les Trois Garçons.

Upstairs, a book-lined study accompanies the dining room on the ground floor, and is the one room that is painted a dark colour. "It's one of my favourite little spots," says Lewis. "I love books, they're like part of the family."

From there, stairs lead up to the first floor and the house's double whammy of a drawing room: two cavernous, lofty-ceilinged spaces with five sets of full-height windows looking on to the treetops of the square.

"When we found it, the ceilings had been lowered, the rooms had been partitioned and there was a revolting mezzanine over the stairwell," says Lewis.

"The people who lived here before had decreased the volume, so we just opened it up and reinstated what had been there earlier."

Dark-stained reclaimed parquet flooring contrasts with the white walls, making a chic backdrop for two seating areas defined by oversized sofas - cream and crisp Maxalto at one end, grey and loungey B&B Italia at the other - and Lewis's collection of vintage lamps and tables.

It all looks perfect, but Lewis will never consider it 'finished', and enjoys hunting for her next additions - currently, a shade for the lamp she has just bought for the drawing room, and new dining chairs for the kitchen.

"My taste changes. I wouldn't feel comfortable in a house that was just" - she clicks her fingers - "done. A house grows with you; it's a work in progress."