"I have the safety of my private life, and I am very protective of that," insists the rock star's daughter, dressed in a T-shirt and blazer, her strawberry blond hair up in a casual ponytail. "At weekends I ride my horse. And after work I bathe my kids and put them to bed."
McCartney, in town in May at the end of an Asian tour promoting her label, has been joined in Hong Kong by close friend Kate Moss. We are sitting unobtrusively at the back of the MO Bar, in the Landmark Mandarin Oriental hotel, where no one seems to recognise the daughter of Sir Paul McCartney, one quarter of arguably the most famous band ever to have strapped on guitars.
"I've had it all my life, obviously, so it's something that I try not to pay too much attention to," says McCartney, of being the offspring of a Beatle. "It's just about trying to get on with it and doing the best that I can. It would be stupid to say it didn't slam some doors and create some preconceived ideas of me. But at the same time it opened a lot of avenues and opportunities for me."
Both McCartney's parents - her mother was the late photographer/musician/animal-rights activist Linda McCartney - were influential in shaping her sense of style. As a child, for example, she remembers discovering glittery knee-high platforms and little vintage floral dresses in her mother's wardrobe.
"With dad it was obviously the Savile Row suits and funky T-shirts. Then there were [mum's] bespoke suits; women didn't wear men's tailoring at that stage. In fact, she was really a pioneer of that.
"The psychological side of fashion has always driven me," McCartney says. "Even when I was really young, I didn't want to be a designer because, 'woah, fashion is so glamorous'. It was about … how it makes you feel and how it's such a huge reflection of who you are."
McCartney's outfits are designed for women to navigate the city in, to holiday in and even to do the school run in. Last month she expanded her denim line and her ongoing sportswear collaboration with Adidas is proving exceptionally popular.
"A lot of houses think they are superior to their clients, but I really want to serve these women," she says.
Whether in a cotton mesh and silk panelled dress or a masculine oversized coat with soft girlish lining, comfort and sportiness have become McCartney's calling cards in the world of high fashion.
"But it can take me three hours to decide on 2mm of length on a skirt," she says. "I am very aware of every minute detail."
Living between London and the Wiltshire countryside, and having grown up on an organic farm, McCartney imbues her fashion with a sense of freedom. It's her effortlessness - a way of being feminine without being fussy, and being masculine without being butch - that has earned her many fans.
"[Dualism] is in everything in my life. At my home, you'll see a beautiful painting on the wall and underneath it a weird 1970s sculpture. I can't help being that way."
Brought up vegetarian by her mother - who created the hugely popular Linda McCartney range of meat-free foods - Stella has championed the cause fiercely in her fashion.
"I have never, ever used leather or fur for fashion," she says, her pale blue eyes widening, making her look younger than her 41 years. "From day one, I was never going to compromise or be hypocritical. I don't eat animals for ethical reasons; why would I kill them to make a handbag?"
Nevertheless, she says, it's important that her handbags feel and look as though they will last a lifetime, as leather should.
"Ninety per cent of my customers have no idea that it's not a leather bag," she says. "Yesterday, I was doing the event here and there were women picking up my Falabella bag and going, 'This is leather, right?' They really didn't understand it at first, but I find that exciting.
"I think it probably does come from being brought up in a different way," adds McCartney, who also eschews PVC. "Slowly everyone that I work with understands it and they grow to be very proud. It's certainly a very modern way to approach the fashion industry."
She has cleverly changed the face of "ethical fashion", helping to show there's more to it than Birkenstock-shod women in burlap sacks and grubby friendship bracelets.
"For me, [being ethical] is all about pushing things forward. Fashion should be about change and not just the new silhouette or colour that season. It's about the newness of material, like developing a biodegradable, embossed faux suede or working on new methods for manufacturing that make less waste or use less water.
"I think that waste comes more into play when it's high-street fashion, where you can buy something for 10 dollars and keep it for two weeks. What I'm doing is not disposable. It might cost more, but buying one expensive item that will last is more adult and responsible than buying 20 things that will soon end up in the bin.
"It's a long-term investment," she says, adding that the life cycle of an item can be even longer than your own if you pass it on; which is made all the more possible by her focus on creating designs that work well for many age groups.
Critical of fashion's culture of the "24/7 slog", McCartney encourages her small team to have balanced lives and spend time with friends and family. She herself - with her husband, entrepreneur Alasdhair Willis - has four children to return home to.
"The fashion industry has this quite relentless [pace]; it stems from the top. But I believe that if you are happy in your soul, not exhausted, and feed yourself in other areas, then you are better in the workplace."
It has taken McCartney some years to achieve this comfortable dualism: at home in both the city and the country; on the back of a horse or in front of an attentive audience at a celebrity bash; being an earth mother and a principled style setter.
After attending state school at the insistence of her parents, McCartney studied fashion design at London's Central Saint Martins College of Arts and Design. She was the envy of her classmates when, in 1995, friends Moss and Naomi Campbell turned up to model her graduation show.
She started her own fashion label straight away and made her first sale to a store called Tokio, which had two outlets, one in Tokyo and one in London. After an initial high, however, running the label solo became overwhelming. There was high demand, orders started rolling in and she found it hard to keep up.
"If anyone has anything from that first collection, it was handmade by me in my garage," she laughs. "It was me and two part-time people in this one room - and I didn't really know how to do it: getting all the material, ordering in and manufacturing. So, I decided I was going to set this down for a while because I wasn't capable of doing it justice - I decided to go away and come back to it."
She was then tapped, at the age of 25, to be Karl Lagerfeld's successor at French label Chloé. As McCartney left for Paris, in 1997, the decision elicited shock and derision from certain industry insiders. They were soon silenced, however, by collections that proved to be fresh and commercially successful.
Having interned with Christian Lacroix's couture house at the age of 15, relearning the French way of creating fashion was to be of great benefit to her.
"To work with the best ateliers, mills and artisans, that access was, from a creative point of view, incredibly eye-opening," she says.
In 2001, a more experienced McCartney returned to London to relaunch her label, with backing from the Gucci Group (before it became PPR and later Kering) adding institutional clout to her name. Despite being a conglomerate focused on the bottom line, the group supported McCartney's no leather or fur rule. There was no negotiation on this, she recalls. "It was a given fact that this is how I work.
"The relationship between creativity and business is very fragile in any industry," says McCartney. "From day one I decided and said that I wouldn't give up control of my name and company, so we could either talk from that stance or not at all."
The result was 50:50 ownership and the only truly co-owned brand in the luxury group's portfolio.
Since then, the label has grown stronger, bigger, more international and definitely more influential. Skincare, perfume, lingerie and childrenswear lines followed. McCartney's products are available in 50 countries and in several hundred stores worldwide.
Even Queen Elizabeth II is impressed - this year the monarch bestowed on McCartney an OBE (Order of the British Empire) medal.
"I also liked getting on to the  Time 100 [most influential people in the world] list," she says. "I'm half American, so that was nice for the American side of my family.
"My mum had just such a cool sense of style," McCartney says of the woman who influenced her worldview most, introduced her to vegetarianism and ignited in her a passion for activism - made her who she is, essentially. "She didn't really wear make-up, she used to cut her own hair and was effortless and very true to herself. It wasn't just the way she looked; mum influenced me so much in a long-term approach.
"[As a result] I don't want women to wear my clothes and feel dictated to, and that if they don't have this handbag, then they're not cool enough," adds McCartney.
"It's really important to me to break down those myths of fashion."