Consider the bizarreness of the Olsen twins' life. They're born in June 1986 on, as it happens, Friday the 13th. Ashley arrives first and two minutes later, there's Mary-Kate - non-identical Gemini sisters for Trent, aged two. When they're about seven months old, one of those friends with which this sort of story is always populated suggests that the Olsen parents - Dave, a mortgage banker, and Jarnette, a former ballet dancer - send photos to a casting director. A television show in pre-production needs a baby and Californian labour laws mean that one tot is more usefully played by twins.

The Olsens oblige. "Horrible family photos," says Dave, in a 2003 documentary, adding, in the honourable tradition of amazed showbiz parents, "It was an absolute fluke." The twins join nine other sets at a casting session. They're the only ones who don't cry, who don't mind if strangers pick them up.

Filming starts immediately. The show, called Full House, is almost cancelled early on and Jarnette isn't happy with the disruption to family life. But it lasts for eight seasons, is sold widely overseas (in Estonia it's Lastega Kodus, in Poland Pelna Chata, to excitable Swedes it's Fullt Hus!) and the twins become famous, although they continue to share a single credit - Mary-Kate Ashley Olsen - long after besotted audiences can tell them apart. At the height of their fame, they're American television's second most-popular stars; the most popular, of course, is Bill Cosby.

Scripts are written around their real-life milestones: the first tooth, the first word, the first step. Their parents hire an entertainment lawyer called Robert Thorne to renegotiate their contracts. When they're seven, he helps them set up Dualstar Entertainment, and soon they've built a brand-licensing empire selling videos, clothing, books, bags and bedding to "tweens", a hitherto unmined consumer demographic aged between eight and 12.

By 10, they're the youngest self-made millionaires in American history. By 13, they're executive producers of their own films. A frequent comparison - a goal to strive for, at least in that pre-incarceration era - is with Martha Stewart.

By the time they're 17, according to Thorne, their chief executive, "They control all the decisions, everything they do - products, projects, media, fashion." It's soon clear that he's not exaggerating. On their 18th birthday, they become co-presidents of Dualstar; eight months later, Thorne's gone. The twins are grown-up. Now they're in charge.

After that, life becomes more complicated.

IF, LIKE ME, YOU'VE NEVER seen Full House and the Olsens have only registered as a dim blip on your cultural radar, YouTube is an invaluable asset. There they continue their lives as very cute babies and not very good actors. They stare with adorable blankness at the camera crew, they're jiggled in actors' arms as a prompt to say their lines and, once they've learned to walk, the show's dramatic tension is considerably heightened as they totter about the set. Farting, playing with rubber dolls, scribbling penises on scripts - these were the ways (according to Bob Saget, who played their father and last year published his autobiography, Dirty Daddy) that the three adult males who starred in the show dealt with the pressures of acting alongside America's sweethearts.

The girls, apparently, were oblivious. There's a line in a documentary about the moment when Full House looked as if it might be rapidly emptying after season one. "[The network] decided to see the Olsen twins grow up on television, something that had never been attempted before." That would have been early 1988, a decade before The Truman Show. You find yourself musing on Truman's career choices after he managed to escape. (Collage artist? Set designer? Sailor?)

The Olsens focused on fashion, however, which is why they were in Hong Kong recently. Since 2006, they've made a "butt-clenchingly expensive" (according to The Telegraph newspaper) range of clothing called The Row. Lane Crawford has just redesigned part of its IFC flagship store and throughout this month and next, The Row is taking pride of place on the third floor, where the Home section used to be, near the new jewellery displays. I'm giving directions because you won't notice it immediately. The Council of Fashion Designers of America, which awarded the twins their womenswear designer of the year title last month for the second time, describes the range as "anonymous luxury". Maybe that's tautology: maybe, when you've grown up as the Olsens have, anonymity is the luxury.

Discussing The Row with them, therefore, is always going to be problematic. When the twins turned 18 (a birthday that was anticipated, on some websites, with a clock counting down the seconds until the Olsens became "legal", i.e. sexually of age), they instantly became paparazzi fodder and had a horrible time. There were stories about substance abuse, treatment for eating issues, Heath Ledger's death; and Mary-Kate is still subject to regular speculation about her wedding to Olivier Sarkozy, the 46-year-old half-brother of ex-French president Nicolas, which has secretly taken place or is secretly about to take place or is secretly never taking place, depending on which website you favour.

As a result, they rarely talk to the press except about fashion and even then, with limitations. On the list of advance questions that have to be emailed over, accompanied by my bio (a professional first), I included one wondering who gives them advice and one asking how much they've, personally, liaised with Lane Crawford on the project. Word comes through that they'd rather skip those. On YouTube, there's a clip of Ashley, at 18, reviewing her childhood and coolly remarking that they looked "like cute little chimpanzees". Perhaps it's no surprise that the twins wish, in their turn, to make performing monkeys of the media.

IT'S HALF AN HOUR BEFORE our scheduled meeting but the Olsens are already waiting. Two other journalists have separately gone in, been dealt with and dispatched. This, believe me, is unheard-of swiftness. The twins, as Lane Crawford's public relations manager delicately puts it, are "very concise".

Outside the Platinum Suite, reserved for the store's exclusive spenders, a couple of guys from a local security firm are standing guard with the cheerful air of men who've had more onerous duties. Inside, at the far end of the room, two small, wan females are huddled under shawls. (Two women from their team melt silently away and seat themselves nearby.) The dual stars aren't exactly twinkling. They've flown in from New York this morning and the room temperature, as is the Hong Kong fashion, is on the chilly side.

Mind you, this scenario - the shivering, swaddled twins - tends to recur in other locations and at other interviews, too. Mary-Kate has previously explained that her much-copied homeless, grunge-chic look was actually a response to the twins' move from California to New York in 2004. "For me it was so cold, like the wind chill," she told Style.com. "How can you not put on 20 things when you're going from Los Angeles to walking through the snow?"

A reasonable question, although it doesn't explain the excessive wrappings in indoor public situations; those layers suggest clothing as shield not style.

The pair are tiny, a word they often use to define themselves. Ashley is about 155cm, Mary-Kate a little shorter. That double dinkiness is a potent force; it was the source of their appeal in childhood but you can see how it might ensnare an adult. Incredibly, there's a scene in season three of Full House involving the composition of a diet jingle; a clip of one of the twins, then aged almost three, poignantly lisping "Bye, bye fat!" on demand should give any stage-parent pause.

And if you ask, which I do, the dull but approved question about the first clothes they ever made, Mary-Kate says, in a flat voice, how they'd always made them when they were growing up "because we're so petite". By "made", she doesn't mean stitching frocks on a Singer in the bedroom; the girls, especially when they did their own films and videos, wore designer clothes that had to be cut down to fit.

Ashley adds, "We had a fun time doing it. We had to pick 60 outfits a week."

Was that fun?

Silence.

Mary-Kate: "It was fun when we got creative control. We'd had a few brands before starting The Row, so I guess being aware of the market helped. The Row was a passion project."

They'd certainly had merchandising experience. An early range of clothing in their name was sold at Wal-Mart and at one point, theirs was the second-biggest tween brand in the world (Disney being No1). But they've had no fashion training, they don't sketch, presumably various wardrobe departments retailored those baggy designer clothes, and you really have to wonder who advises them …

Mary-Kate (petite edge to her voice): "When people ask how involved we are - you know, 'Do you really design?' - it's not a great question. There's a lot of work that we do. It's been a 10-year run."

Ashley (placatory, good-cop tone): "I don't think you know anything unless you try it yourself. The exciting thing is entering the industry and learning every day. Mary-Kate and I love to learn."

Although they didn't complete their first year at New York University, that is surely true. After all, they weren't the only cute toddler-twins on Full House. There were also Nicky and Alex, played by Dylan and Blake Tuomy-Wilhoit. Blake is now a fireman, in Atlanta, and Dylan's a sound-technician, and I'm fairly certain neither has ever featured on Forbes' Celebrity 100 list.

And although girls loved Mary-Kate and Ashley - the real ones, not the cartoon versions in a spin-off animation series that was a flop - and wanted to dress like them, fan-devotion can't be the only explanation for their current fashion success. Apart from the fact that few of those tweens could afford The Row, the clothes were, literally, anonymous in the beginning.

Ashley: "We wanted to see if we could sell without a label that people knew. We sold them to Barneys [department store], no press, no PR. People bought it. And being able to sell the product spoke for itself."

So, they're like J.K. Rowling, who wrote a non-Harry Potter book under a different name to prove she could? This, admittedly left-field, comparison is greeted with total blankness (although I find myself thinking what an excellent, indeed desirable, fashion concept a cloak of invisibility is).

Mary-Kate (eventually): "We love what we do. People that are not in the industry don't necessarily know how much work goes into it. Fashion is non-stop, there isn't a break."

The name supposedly refers to Savile Row, and its association with tailoring, but, when I first read it, I wondered if it was a punning refer-ence to sibling arguments. Ashley, on hearing this, unexpectedly grins and says: "That's funny. I liked that version, too." She tries it out: "The fight. It was easier to say that it referred to Savile Row but for me - I liked that other aspect."

Oh, really? …

But Mary-Kate has leaned forward and is stating, not in the least feebly, "I think when Ashley says that, it's her sense of humour."

Asked what they're both wearing (it's difficult to penetrate the tussock of borrowed shawls), they exchange glances plus teeny-weeny sniggers, and reply, "The Row." Pause. Eventually Mary-Kate concedes that her trousers, being made of denim - definitely a non-Row fabric - are Elizabeth and James, another of their fashion labels, supposedly named after their other siblings.

Elizabeth is their younger sister, now 26, a respected film actress ( Martha Marcy May Marlene), most recently seen in Avengers: Age of Ultron, as the Scarlet Witch. Their older brother, though, is called Trent.

"An article got it wrong about the names being our siblings," sighs Mary-Kate. "The concept is about masculine/feminine attitudes." So, where did the name James come from? Maybe he's one of their half-siblings? (The Olsen parents divorced when the girls were 10, and Dave remarried.) Or maybe James is Trent's other name (which, puzzlingly, turns out to be the case)?

Mary-Kate, however, has had enough.

"It doesn't matter," she says crossly. "Why are we talking about Elizabeth and James? We're here to talk about The Row."

THE CLOTHES ARE BEAUTIFUL, a homage to simplicity in an overwrought world. If Jil Sander and Hermès had a love-child, it would be The Row. The target customers, according to the twins, are women in their 40s or 50s who are, as a Lane Crawford spokesman puts it, "minimalist Céline types, not Diane von Furstenberg customers".

Also, types with plenty of money; The Row's famous $39,000 alligator backpack is on sale here, and those would be US dollars. Everyone mentions the cost, the fact that a single head-to-toe outfit can be the equivalent of buying a car.

"The prices are honest prices," says Mary-Kate. "It's about the quality, the fabric."

The following day they're going to meet invited customers for a little styling session. (No press allowed, obviously.) Then they're off to Shanghai for a day and a half to do the same thing. When I ask why they don't give themselves more time, Mary-Kate says, "We're in the middle of our spring runway show, we have to get back to work."

Ashley adds, "The pressure comes from ourselves. We're not part of some big house where we have to hit certain numbers."

Not a full-on house, perhaps; but you feel the striving.

"We're perfectionists," says Mary-Kate.

Have they seen Dior and I? This question, asked on a whim, is like producing a candle: Mary-Kate lights up, sits up, leans forward. She saw it on the plane, Ashley didn't. "But I told her about it already. Raf [Simons, Dior's creative director] is amazing, the team is amazing."

It's really a film about passions, particularly those of the usually unseen people toiling (and toile-ing) in the atelier.

"It's always about the atelier," the twins say, in unison. When Mary-Kate talks about Dior's workers I'm struck by the close attention she's paid to their tasks. Do they have people like that?

Ashley says, smiling, "Ours are probably the funkier version." But Mary-Kate is in earnest: "I do believe people are happy, I feel confident in saying that. We all share the same goals and values and it starts from the top."

AFTERWARDS, I GLIMPSE the twins in the store with their people and security team, inspecting some detail. (The selection process for the display has apparently involved many, many emails.) In video clips of their childhood public appearances, they were like animatronic cupcakes, sweetly decorated and displayed so that middle America could drool over them. But, after a while, what you notice is all the touching - the prodding, the cuddling, the fondling. Now, protectively ringed, you can hardly see them as they whip themselves onwards.

When I'd told Mary-Kate that, moved by its passion, I'd started to cry two-thirds of the way through Dior and I, she'd simply replied, "I was too tired to cry."