Erin O'Connor's beauty is so startling, so offensively gobsmacking that I do the only adult, sensible thing when faced with it: run away.

Her head, a helmet of dark chocolate hair framing a face made from the arches of an Oxford college, appears through banisters as she ascends the stairs of the Covent Garden Hotel. It is too much: outrageous, sneering cheekbones, bold black eyebrows and a plunging, Gallic nose so haughty it could Elizabeth I status anxiety. Winded, I bolt out of the room and cower behind a sofa in the library. But there's no escape.

The head appears again, this time skimming the doorframe – her six-feet-nothing perched on three inches of tomato-red heels. In between looms a body of mesmeric proportions: the highest waist and longest legs you'll see outside a circus. Elegant, everlasting arms as if Sylvie Guillem had enjoyed a second growth spurt. And skin. Oh, her skin. It appears to have been passed down by Snow White with a note saying, 'Make Cleopatra look haggard'.

A hand is extended with a huge, soft smile. Oh God, she's going to be nice as well. O'Connor banishes her agent and press officer (a rare joy) and spends the next 52 minutes attempting to run away from my questions. The Garbo of modelling, it transpires, can sniff out interviewers' tricks like a drugs squad hound. Well, some of the time.

Is Britain's most private supermodel relieved not to have endured the paparazzi-frenzied life of Kate Moss? She pauses, spots the potential, 'I'm Glad I'm Not Kate Moss' headline and offers humility instead:

"Having worked with her lots of times I can never quite get my head round the fact we're sharing work space together: she's from another planet, so exotic, so defiantly different." An embarrassed grimace spreads across her face as she admits to trying to "emulate" Moss as a teenager.

"Remember that baby doll dress phase with the [Adidas] Gazelles? I got both, plucked all my eyebrows out and looked like Olive Oyl."

And when I ask how she feels about John Galliano making tentative steps back into the industry after his conviction for anti-Semitic abuse (something of a no-win question), she replies: "I'm pleased that John is helping himself to be well again and that's all I can say".

But when her feelings are strong enough, caution – after brief attempts at diplomacy – is abandoned like a first wife. The campaign to ban both Page 3 and lads' mags is gaining momentum. As the reverse kind of model, what does she think?

"I would rather not comment," she says, before saying precisely what she thinks: "I do have an opinion but it's been the same one since before mine [her breasts] arrived: I can't believe boobs are news in this day and age."

A preamble follows about her father, who works in a welding factory, being "the best feminist" she knows before agreeing that she, too, is a feminist. "How could I not be in this day and age?"

O'Connor says: 'I understood early on that I was not the best-looking girl in the room.' (Kalpesh Lathigra)
Her feelings punch through with rather more pathos as I broach Alexander McQueen. O'Connor, now aged 35, was his muse, modelling in many of his most revolutionary shows, evoking such counter-beauties as Pierrot, Joan of Arc and a bird trapped in a lunatic asylum. How did his suicide in 2010 affect her?

"That's such a private topic…" she begins, inhaling sharply through her nostrils, before carrying on: "He was a normal man consumed by brilliance which he somehow managed to translate into real life. It was a gift to work with him and grow up alongside him. We had a real, responsive relationship, it was a match made in heaven."

Her eyes glisten. Her voice, already as gentle and low as a bass flute, drops further.

"He took my career in a specific direction – I didn't get to play the bride but I got to play Joan of Arc. It was inspiring." Does she miss that? She inhales again and straightens her back.

"I can't be sentimental. I have to move forward, you cannot repeat those shows, you cannot go back…"

We move on, the discussion turns to the early years of her career and one word keeps cropping up, a clue perhaps to her fierce self-protection: boundaries. As a teenage model in the 1990s, did anyone invade hers?

"I was in a room, changing," she says, glancing down, "and there was no privacy and as I was undressing, my body was being discussed very audibly. It didn't matter what their angle was, whether it was complimentary or not. I asked for privacy and I wasn't given it. So I put my clothes back on and walked out."

O'Connor doesn't name names, only that by leaving the casting session she "didn't get the show" which cost her "overnight status". But no matter: "I got so much more in the end – I got to take my dignity with me. I prevailed in that moment."

She's been prevailing ever since. Her success may not have been overnight, but it was hardly long-fought. Raised in Brownhills in the West Midlands, she was spotted by a model agent at the Clothes Show Live, aged 16.

"I still can't quite grasp how that very ordinary day had such an extraordinary effect on the rest of my life," she says.

Within two years she was storming the runways of Gucci, Chanel, Donna Karan, Fendi, Versace and Valentino. Within three she'd won the model lottery: the cover of Vogue.

"I understood early on that I was not the best-looking girl in the room. But I knew my advantage was a hard work ethic and I was ambitious: I knew I could be a great model."

She was right. In 1999, O'Connor was named Model of the Year at the Elle Style Awards, a beanpole colossus bestride the commercial and the editorial: the 'androgynous' antithesis of Kate Moss. Morticia Addams with a flapper bob.

Marks and Spencer, hardly the emblem of fashion edge, signed her up in 2006, just as the size-zero debate was erupting. Images of O'Connor filled front pages to illustrate the skeletal phenomenon. (In person, she doesn't look unhealthily thin, merely unusually long). But discussion of underweight models has abated recently. Is that because things have changed or because everyone's given up?

"There are groups who would agree with both of those statements," she says. "I've been on both sides: the victim and the villain. I was the victimised model and everything from my weight to my fertility was held up for discussion. And then I was the person that could garner some kind of positive outcome, by taking on the role of vice chairman of the British Fashion Council and becoming an activist of body image."

In 2007, O'Connor set up the Model Sanctuary, a space during fashion week where models can seek advice from nutritionists and psychotherapists.

"If you start trying to legislate or ask models to come in for medicals and health certificates, you could alienate those who do have problems."

Two years later, she launched All Walks, an organisation devoted to increasing diversity on runways.

"Why should there be one ideal? It feels regressive."

She's hopeful "something worthwhile is beginning to happen". She also doesn't spare the industry her somewhat arch, more general observations, that there is "a fear in fashion that once you unravel the magic there's reallyf nothing there" and "Fashion is such a secret thing – well, it likes to think it is".

The Face, the television series that O'Connor has just filmed, will certainly help demystify modelling, as it searches for a new star. The 'mentors' are O'Connor, Naomi Campbell and Swedish supermodel Caroline Winberg. Why do such a show?

"I've been so self-involved up to this point that I wanted to face the opposite direction," she says. It helped that Campbell, an old friend, had already signed up.

"I didn't want to say no to her, she's a pretty persuasive woman!" Their personalities are "polar opposites".

"I'm a thinker, so I would consider each girl and try to approach them differently. And Naomi was like [adopts a strident voice] 'Get to the point, I'm not a psychologist, you need to know…'."

She laments the "validation" young girls seek from "external environments" and says the aspirants brought out her maternal side. Does this mean you're the Cheryl Cole of the show? A shriek goes up, followed by a comedy Geordie accent.

"Oh Cheryl, she's a gem," she says, adding, deadpan: "I'm about 180cms taller than her."

There is of course a 10-foot irony in a supermodel who shuns publicity coaching wannabes on television. But for O'Connor, the contradiction is also internal.

"It's that, 'Look at me, look at me, DON'T LOOK AT ME' thing," she says, rolling eyes at herself. "I understand you don't always get to choose when people look at you. But I can storm a catwalk, be the tallest in the room and own it, only to cower on the Victoria Line going home."

Much has been made of the bullying O'Connor endured at school on account of her looks. Today, though, she says this "cliché" that she "suffered at the hands of other people" has been "pushed", when in fact it was "self-imposed criticism" from which she chiefly suffered.

"I was just a normal person struggling to come to terms with my expanding self. We all have self-destructive tendencies."

O'Connor with Elizabeth Jagger and Jodie Kidd in 2002 (Rex Features)
The fashion elite has been hit by a dark period in recent years. McQueen's suicide, along with Isabella Blow's – the fashion editor who discovered him – nearly became a grim triptych when supermodel Noémie Lenoir took an overdose in 2010, just months before Galliano's dipsomaniacal implosion. How have you stayed sane, and avoided drink and drugs?

"Fear has been my biggest friend," she says. "Fear of the unknown. Whenever I've been afraid, I've been very self-protective. Mental illness [in fashion] is a huge topic, which we could devote another interview to. But I don't think any of us are exempt from challenges in our lives, especially when we're given a huge amount of freedom. Because I'm sensitive, really sensitive, I'm reminded of who I am all the time and I'm not prepared to put that in jeopardy."

Fashion, in fact, proved O'Connor's salvation, yanking her out of shyness.

"What I do with all that sensitivity is to get out on stage and be a performer. I'm addicted to that, completely liberated by it. I have no fear. I come off stage and think, 'What just happened out there?'."

Perched on the coach, with one leg turned out like a ballerina and gesticulating floridly from the wrist, such softness and femininity exudes from her that the androgynous tag seems ludicrous.

"You're the first person who's ever said that me," she says, sadly. "I love being a woman. My interpretation might be different, but I embrace womanhood. I'm comfortable with who I am. I think I've earnt it having other people's opinions of me reflected back."

But the woman Karl Lagerfeld described as "one of the best models in the world" still isn't invulnerable to our narrow beauty constructs.

"Yeah, I've still got a prominent nose and, sure, I have days when I'm not infallible to thinking, 'God I wish my boobs were differently shaped'. But I don't feel obliged to change myself for anybody. No Botox for me. No nothing." Would you like to be a busty blonde for a day?

"Would you?" she says, laughing. "Of course I would. I'd like to know what they were thinking. I do feel sexy but I'm not overtly sexual." Are men intimated by you?

"Given that I outgrew my first boyfriend, I'd imagine there have been a few men over the years that have struggled," she says, almost succeeding in sounding sympathetic. "But men are good at fronting it."

She's had a partner for "a while", whom she won't name – a "proper grown-up" who isn't in fashion and is "tall" and "not intimidated" by her. She says, "now would be a great time" to have children, but they won't marry first.

"What matters is having the love that I would have hoped for, which I have now. It's not about having the sexy man, it's about the outstanding daddy, too." Speaking of sexy, how do you get your body to look like that?

"Boxing. Three times a week," she says, flexing her bicep and grinning wildly.

I knew there was a reason to run away. Intrusive casting directors, beware.

'The Face' starts on Sky Living HD this Monday at 9pm