Christopher Kane is one of a rare breed of designers who say it like it is.

No flamboyance, no grandiose comparisons. He calls a spade a spade, a frock a frock. "Let's just put it out there," says Kane in his still-intact Lanarkshire accent. "[Fashion] is not rocket science." It's a fair point, but not necessarily one you'd expect one of Britain's most celebrated designers to make.

That's the thing about Kane – what you see is what you get. He has his head firmly screwed on and a strong sense of identity. We meet shortly after his presentation to a select group of people in Harvey Nichols in Edinburgh about his new autumn/winter collection. You can assume there were loyal fans and wealthy customers among the audience, but Kane seems more impressed that his mother is here. "I don't get to come home that often, so my mum comes to see shows and things."

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The Kanes are a close-knit clan, regularly accompanying the family prodigy to awards ceremonies and attending his catwalk shows. Then there's Tammy, the elder sister who, though not here today, is an integral part of Kane's eponymous label. The siblings have become a double act of sorts since the Christopher Kane label was launched in 2006, and are often referred to as London Fashion Week's answer to Donatella and the late Gianni Versace – arguably the most famous brother-sister duo in fashion. Today Kane, one of his own cashmere jumpers casually tied around his waist, is flying solo. Granted, the usual PRs and assistants are around but his right-hand woman, Tammy, is a few hundred miles away in London with her seven month-old daughter Bonnie.

Kane says Tammy is still as much a part of the label as ever. "She was back to work four to six weeks after giving birth." Although he adds, with a hint of guilt, "That child has not had a minute – I feel terrible because the baby has been on the go, she's been around the world, but then babies are so adaptable. As long as they're with their mum or dad they're fine."

Although Kane would happily talk about babies for the next half-hour, we've got other things on the agenda – his stylish creations and ever-growing empire, to be specific.

So, how is the world of Christopher Kane? "I'm here for the 10th anniversary of Harvey Nichols, and we've just finished the show so we're really busy – it's been a month since the spring/summer 2013 show – but it's all good; business is good," he says. "I'm not complaining."

It's fair to say business has been good since Kane's degree show collection in 2006. His story is one you might be familiar with. Young Lanarkshire man moves to London to study at the revered Central St Martins. He catches the eye of tutors, creates what would become one of the most iconic debut catwalk shows by a British designer, and is given a personal audience with American Vogue editor and all-round fashion maven Anna Wintour. Within weeks he is being hailed as the next big thing – the great white hope of London Fashion Week and the most refreshing newcomer since Alexander McQueen and John Galliano.

From the outside it looks like fashion has been gripped by Hurricane Kane, as high-street copycats and other labels look to Kane's vision season after season for the new direction. One minute neon dresses a la Kane are flying off the shelves in a gust of excitement, the next we're all being swept up in waves by the rebellious charm of his leather and crystal creations.

He's fairly level-headed about the experience. "I love my job and I'm really lucky," he concedes. "Fashion is fashion and it is what it is, every other industry is like this too – there's always deadlines and there's always stress. The pressure is good and it moves you on but now we're at the stage where we're not the bright young things. We've been put on a pedestal – we're always mentioned in the same category as Prada and Balenciaga but we don't have their money. But it just shows you we're so determined."

The Kanes – Tammy has as much to do with what appears on the catwalk each season as the man who gave the label his name – are known for their gutsy approach. From the beginning they've done things their own way, paying little attention to the rule book or what others thought they should be doing. Kane even turned down a prestigious job working for Versace in order to develop his own label. "You can be given a plate of gold," he says, "but if it doesn't feel right you don't take it."

Kane went on to accept a consulting role a few years later with the Italian fashion giant, collaborating with Donatella Versace on the company's youthful Versus brand, and now designs several collections every year, for his own label as well as for Versus, not forgetting his successful Topshop collaborations. All this would be impressive by anyone's standards, but when you consider that Kane is just 30 years old and has only been designing professionally for six years, his achievements are dizzying.

So what does Kane think is the secret to his success? The Scottish work ethic apparently. "I think being from Scotland and growing up here, it's really great," he says. "You have a mentality and it's instilled in you from an early age, to work hard and be committed. You're not in the clouds; you're actually quite grounded – you're normal. In London you go to all these crazy events and you feel so far removed. Honestly, sometimes I think: 'Oh God, this is not my thing.'

"I'm not from anywhere else than Scotland and Newarthill [near Motherwell]. My mum and dad were working class, blah, blah, blah, and I'm always going to feel like that. And I'm not going to feel fake or false or anything like that because it's not in me."

Then there's his sister, without whom Kane says he could not have done all this. "Tammy has been hands-on throughout the whole process. We're such a tight team. Me and Tammy work so closely together. We think alike. She's so on the job and she loves what she does – she feels bad having a sick day. I'm so grateful for Tammy and I don't know how other people do this without [someone like her]. Tammy does exactly the same as me – we're both 100% creative. I'll put out ideas and she'll put out ideas and she's amazing. I am lucky she's my sister and we're very intuitive."

The current Christopher Kane collection, autumn/winter 2012, includes a series of purple-accented garments and printed separates that were inspired by a lilac bag strap that Kane found.

The spring/summer 2013 collection, which earned the approval of Wintour and the Prime Minister's wife Samantha Cameron at London Fashion Week, featured all-white ensembles clipped together with over-sized bolts. If you read the reviews, this "fantastic, so clever" spring collection was inspired by Mary Shelley's Frankenstein, although Kane admits the coverage doesn't always reflect his true inspiration.

"You have to tell journalists something," he says. "They like for it to have a whole story when it's not actually about that – it's about the fabric. It gets delivered and it looks amazing. Sometimes people like to make something out of something it's not. People love a story and it will always be like that. Sometimes backstage I think of something and I just say it. It's nonsense but it gives people something to write."

Wherever the ideas come from – whatever the truth in those reviews – there's no question the Kane vision continues to strike a chord with the moneyed fashion-buying public. His clothes – dresses, for example, often cost more than £1000 – sell out in boutiques and he remains one of the few designers at London Fashion Week who can expect an audience of international buyers and press.

Business, as Kane says, is good. But with success comes responsibility. His label, based in north-east London, employs 25 people, making Kane as much an entrepreneur as he is a designer. "I have the responsibility of paying wages," he says. "It's tough. It's a proper business – it's a functioning business and it's oiled every week. It's a working machine." Is being good at business as important as his design work? "Yes, it's very important and I learned that quickly," he says. "You have to understand the demand and the things that are changing."

Kane, the man who has been able to predict which way the wind will blow each season, now senses a change for his label. The brand's profile has been growing steadily, but Kane thinks they're reaching a plateau. To get off it and become a bigger brand they will need investment. Would he ever consider selling his label to one of the conglomerates? He shrugs. "It's always on the horizon and you can't rule it out," he says. "When you hit a glass ceiling like we're coming to, you have to look forward. It's only natural – it's the progression of a brand. You have to have major infrastructure behind it to go forward, and the knowledge and expertise."

Kane's dream – the big vision – is to transform his brand into something bigger. Something iconic. "It's having the shops, having the world of - like Chanel, Prada, Versace," he says. "It's what you aspire to – having that household name. Every designer might not admit it, but that's what they want." n