The elegant woman who has just opened the townhouse door looks nothing like April Crichton, the person I'm scheduled to meet and the creative director of Sonia Rykiel.

More precisely, she doesn't look like the April Crichton I've seen on the internet. The nose is different for a start – not so long but thin, elegant and straight. Then there's the hair – a thick, chestnut, curly mane in the photographs but straighter and lighter in real life. The face is slimmer too and the cheekbones not quite so pronounced. The eyes, though still brown, are rounder and softer.

It's my mistake, though. This is definitely Crichton – she says so herself. "Hi, I'm April," she says, hand extended. "Come on in." We wander through the hallway of her home in the west end of Glasgow, past modern art (more on that later) and through into the living room. There's more art on the walls, most of it colourful and abstract, and a few concrete sculptures masquerading as side tables next to the mismatching sofas.

Jackets off and formalities over, we settle down on opposite seats. "Can I get you a tea?" asks Crichton. She does. Earl Grey, poured from a handsome teapot.

Crichton is a fashion designer, and a very good one. She's responsible for the Paris-based label Sonia Rykiel, a brand which has become synonymous with two things: brightly-coloured knitwear and a near obsessive use of stripes. She also oversees the brand's more affordable sister label Sonia by Sonia Rykiel (again, more of the same quirky, colourful stuff). For two days a week she's in Paris, where she has a flat, working with the label's design teams. The rest of the week Crichton designs from home in Glasgow. She was appointed creative director of Sonia Rykiel last September but has been working with the label and its founder for the past 22 years.

Yet most people have never heard of Crichton. Most people "don't know I exist", she says. There's no hint of disappointment, though – anonymity suits her. "I don't feel the big celebrity designer name status is something I'm interested in," says Crichton. "I want to focus on the product and make the garments desirable."

There are more than a few misconceptions about Crichton. First of all, those images on the internet are actually Nathalie Rykiel, Sonia's daughter and vice-chair of the company's board. It seems photographs of Crichton are so rare that some people have assumed Nathalie and Crichton are the same person. "I work closely with Nathalie," says Crichton.

Then there's the Scottish connection. The designer, 44, lives with her husband Toby Webster, the director of The Modern Institute, arguably Britain's most successful and influential art gallery and agency, plus their children Honey, 10, eight year-old Lyle and Vita, four. Crichton was born in Yorkshire to Scottish parents but says she considers herself Scottish. Which is just as well, as she's been nominated for Designer of the Year at the 2012 Scottish Fashion Awards.

It wasn't until the mid 1980s that Crichton moved to Scotland, after her school art teacher suggested she apply to Edinburgh College of Art. "I felt happy with that because I was leaving home for the first time and my grandparents lived in Edinburgh, so I had connections – my parents are from there originally. I went there and loved it."

The move to the Scottish capital changed Crichton's life, partly because that's where she discovered her passion for fashion, but mostly because she befriended a student called Emma Webster. "I used to come to Glasgow with Emma [for nights out] because there were better clubs, and I met her brother Toby and he's now my husband." Their relationship, by the sounds of it, has always been one of old-school romance. "Toby and I used to write fantastic letters to each other with drawings on big sheets of paper – it was very romantic," Crichton says. "We hooked up again when I was in Paris and he would get the bus and come and see me and we'd hang out, and we've been together since."

We're getting a bit ahead of ourselves though. Crichton's not moved to Paris in the story yet. She won't do that for a few years. First of all she has to complete her art course at Edinburgh, do printmaking and take some "fantastic life classes" before deciding fashion would be her calling.

Crichton thought about staying at Edinburgh to study fashion, but the lure of Central Saint Martins proved too strong. "I felt I needed to be in London so I decided to apply to Saint Martins, which I'd read about and my hero John Galliano had gone there," she explains. "It was in The Face and Blitz magazine – it was all about the clubs, so that was where I wanted to go. I would make outfits, put jumpers on my legs. Fashion was a way of expressing myself and I loved it and it was where my heart was."

While Crichton graduated from Central Saint Martins in 1989, it wasn't until a chance encounter that she got her first job. "I met somebody in London who I admired and she had just been working for Sonia [Rykiel] and she saw my portfolio," Crichton says. "I'd been wondering what to do and where to go, and she said: 'Go along to Rykiel – they'd like you.' And I did. Sonia said yes there and then, which was absolutely fantastic."

The sounds of someone banging and shuffling emerge in the background. They're coming from downstairs where Betty, Crichton's cleaner, is tidying up the enormous bespoke kitchen. The family's Burmese cats, Locky and Minty, amble into the living room. One curls up near the window while the other continues to parade around the floor as though on patrol.

The conversation turns to Sonia Rykiel herself, who recently revealed she has been suffering from Parkinson's disease for the past 15 years. In her new book, N'oubliez Pas Que Je Joue, Rykiel, who is 81, writes: "I don't want to show my pain. I resisted, I hesitated, I tried to be invisible, to pretend nothing was wrong. It's impossible, it's not like me."

Crichton was at the label when Rykiel was diagnosed. "She's physically less able and that is frustrating for her. It's upsetting for everyone to see that happening because she's always been extremely present, and work is her life. She's always been industrious: she's written books and founded literary societies and cigar-smoking clubs. So not being able to be in the office and finding it so physically draining has been a terrible strain on her."

Crichton retains a huge amount of respect for Rykiel. She describes her as "an amazing woman" and I get the impression Crichton looks up to her, both personally and professionally. "When I was a student at Saint Martins I managed to see a Sonia Rykiel show and I was impressed," Crichton says. "I was blown away by the drama of the catwalk. She had all of these girls in knit sweaters in this huge spectrum of colours. It was amazing – a spectacular show with that spirit of excitement, drama and joie de vivre."

In the mid 1990s, after four not-so happy years living in Paris, Rykiel allowed Crichton to move to London and work remotely so she could be closer to Webster. "I always felt it [Paris] wasn't that young a city," she says. "I felt like I was at Granny's house – it felt a bit heavy. The move was also for being with Toby. There's this great kind of family atmosphere at Rykiel and she understood all that, and so she allowed me to go back to London and I worked freelance. Thinking more about how the situation arose and how she allowed me to do that and grow, I have huge respect for her."

Crichton may admire her old boss but there's no doubt she is her own woman. Rykiel – flamed-haired, bold and always willing to speak her mind publicly – is larger than life, whereas Crichton seems less keen to be in the Paris spotlight. "The fashion world - it's not for me," she says.

Crichton's reluctance to be at the heart of the industry fits with the kind of person she is – quiet and private, someone who doesn't want to be the centre of attention and doesn't like to show off about her work. It's clear even talking about herself holds little appeal. "The press side I can do without," she says. "You obviously need to do a bit to communicate but it's not my thing. I love to create and I love to draw and I love to express my ideas and I love to see people wearing my clothes."

This desire to blend into the background might go some way to explaining why Crichton was only announced as creative director of Sonia Rykiel last year. In truth she has been doing the job for about two and a half years. She was previously head designer at Sonia by Sonia Rykiel, after coming up with the idea for that label in the late 1990s.

The doorbell rings – the photographer has arrived to take Crichton's portrait. She leads him into the lounge where the talk turns to the Webster family's art collection, Crichton spooling off the names of a few of the contemporary artists whose work is hanging around the house. In the hall we stop to have a peek at a David Shrigley drawing of a well-endowed though slightly scrawny naked man, complete with amusing poem about wives and marriage. "Everyone has a chuckle at that," says Crichton.

If the fashion world isn't her cup of tea, is the art world? "I totally have another life, and it's important to me." Does this other world – the world of art – inspire her own work? "Totally. We receive a lot of artists here and entertain them, and that's a constant source of inspiration – it's not something I'd get in Paris."

Being a mother is crucial for Crichton too. "Managing a family is a pretty big thing," she says. "I think it's even more important than the job, although I think the two are compatible." Indeed the Sonia Rykiel team sometimes come to Glasgow to source vintage clothes or conduct fittings in Crichton's home. When that doesn't work, and school holidays permit, Crichton takes the children to Paris.

"The kids are interested," she says. "They've always been involved and they've always come to the studio. They pick up some of the language. Vita is really interested and asks: 'What does this mean?' Usually one of them travels with me in the summer and they come into the studio and watch what happens on a day-to-day basis."

But their interest and those little summer trips don't make working between Glasgow and Paris any easier. Every Tuesday Crichton has to say goodbye to her children for a few days and every Tuesday she finds it tough.

"I can't say how hard it is [to leave them], but then when you get there you realise what you're doing it for, and I don't think I'd be the person I am for them if I didn't do it," she explains. "But it's the continual woman's world, and when I had my kids I realised my capacity to manage and still want to do the things to be yourself.

"There are moments when I think: 'What the hell am I doing? I'm not doing anything well.' So I have little things I do when I travel – I listen to music or read a book – so I feel like I'm finishing something. Fashion never ends – it goes on and on and on and on. You're never going to have that moment when you finish anything."

Crichton has just finished something, though – the interview. The photographer, who has been sitting at the other end of the living room for the past 10 minutes, is ready to do his job. Crichton, though, wants to pop upstairs for a minute. I head downstairs, where I meet Betty, who is quietly pottering about. "Did you like April, then?" she asks. Yes, I say, I did. "Good," says Betty, who has the final word. "She's a lovely woman." n

Visit www.soniarykiel.com.