Christina Hendricks hated her high school. When she was 13, her parents moved from the small town of Twin Falls, Idaho, to Fairfax in Virginia because of her father's job with the United States Forest Service. Hendricks felt "uprooted" and resentful. Then she had to start at a new school: Fairfax High.

She stood out from the beginning. In Twin Falls she had been part of a children's theatre group. She wore Birkenstocks and "hippy dresses". She was surprised when she saw the other girls her age in Fairfax "carrying purses [handbags]. I was like, 'Ooh, purses!' To me, only moms had purses. They were much more sophisticated and they were having sex and wearing makeup – all these things that had not happened for me."

From the start, Hendricks was bullied. "We had a locker bay, and every time I went down there to get books out of my locker people would sit on top and spit at me. So I had to have my locker moved because I couldn't go in there… I felt scared in high school. It was like Lord of the Flies. There was always some kid getting pummelled and people cheering."

Hendricks found refuge in the drama department. Acting provided an outlet for a feeling of impotent rage. She became a goth, dying her hair black and purple, shaving it at the back and wearing leather jackets and knee-high Doc Marten boots. Were her clothes a type of armour against what she was experiencing?

"Yeah, exactly," she says, nodding. "My parents would say, 'You're just alienating everyone. You'll never make any friends looking like that.' And I would say, 'I don't want those people to be my friends. I'm never going to be friends with the people who beat up a kid while everyone is cheering them on. I hate them.'"

Christina Hendricks in God's Pocket, Philip Seymour Hoffman's final film. Photograph: PR

Fast-forward 26 years and Christina Hendricks is now one of the most recognised, acclaimed and lusted-after women in the world. Her portrayal of Joan Harris, the sassy 60s secretary who rises to be partner of an advertising agency in the hit series Mad Men, has won her critical plaudits, Emmy nominations and the slathering admiration of a legion of borderline-obsessive fans.

At 39, Hendricks is – unusually for a female celebrity – loved in equal measure by men and women. Much has been made of her extraordinary looks that hark back to a bygone age of glamour – her curves, her auburn hair (dyed red because she loved Anne of Green Gables as a child) and her translucent skin.

A 2010 poll of female readers for Esquire magazine named her "the sexiest woman in the world". Googling her name will throw up websites called things such as "Admiring Christina Hendricks" and a Tumblr devoted to answering the question "What Would Joan Do?", which resolves modern etiquette dilemmas by channelling Hendricks's character in Mad Men (on relationships: "Anyone who you have to convince to be with you isn't worth convincing"). When I told people I was interviewing Hendricks, a female friend pleaded with me to tell her she thought Hendricks was "the ultimate woman since Eve".

"Oh, that's so nice," Hendricks says, pressing her hands to her chest as if accepting a prize. "Thank you."

Has she been shocked at the response to Joan and, by extension, to herself? I imagine it's a lot of pressure to have to live up to being the ultimate woman since Eve. "I guess I was surprised," Hendricks says when we meet in Joe Allen, a basement restaurant in the theatre district on the Upper West Side of Manhattan. "I watched what people responded to in Joan, and she's so many things, but I think it's her strength, resilience and confidence."

Has playing Joan rubbed off on Hendricks's personality?

"I hope so… I've got a little sass in me." She narrows her eyes, tilts her head and smiles in what can only be described as a demonstration of uber-sass. "I probably tend to get my feelings hurt more. I tend to take things personally. But I can only take so much and then I jump back. I have strong survival skills."

The key to Joan is that she establishes her power using her intelligence and the limited means available to her as a woman in an era of institutionalised sexism and unequal pay. I wonder: has Hendricks ever experienced sexism in the acting industry? "Oh sure," she says, matter of factly. "You know, it's difficult in the arts to pinpoint it but there's sexual harassment at work every single day, all day long. Certainly in the respect and position [of women], you feel like, 'Am I allowed to ask these questions or contribute in this way?'… Society has conditioned you that way. As women, we feel we can't ask for things. There's been a lot of research done recently and, more often than not, if a woman goes in to ask for a raise, she'll get it. But she's thinking, 'Do I deserve it? I've got to give a list of why I deserve it.' Whereas a man will just go in and ask for a raise. It's so scary."

Hendricks is promoting her new feature film, God's Pocket, directed by her Mad Men colleague John Slattery (who plays Roger Sterling) and co-starring the late Philip Seymour Hoffman. Hendricks plays Jeanie Scarpato, a trapped housewife who never quite escaped her small town. Jeanie's son dies in the opening scenes and she becomes convinced the town is covering up the real story of his death. Her husband (Seymour Hoffman) tries to find out what really went on. A tale of violence, betrayal and grief ensues.

She says it is difficult watching the film now, knowing that Seymour Hoffman has gone. He died in February, shortly after the film premiered at Sundance. "I was saying to my husband [the actor Geoffrey Arend] that sometimes when you have a friend who passes, it feels very, very final," she says, and her eyes become filmy as she turns away and stares at the tablecloth. "But something about Philip… I keep thinking I'm going to see him again. I guess, when I watch the film now, I feel like it's a celebration of him. I feel lucky to have gotten to work with him. I feel grateful and I feel sad."

Was she shocked by his death?

"I mean, I was because he'd seemed so great… um… and, you know, we'd just been at Sundance with him the week before and he seemed fantastic. I knew he'd had problems in the past but I really did think it was in the past. I was so surprised."

Hendricks readily admits she was intimidated at the prospect of working with a man widely acknowledged to be one of the greatest actors of his generation, but "he was incredibly warm and collaborative" and it helped that Slattery was directing: "It was very nice looking across the room and seeing each other's faces," she says. "A little bit of reassurance in a sea of uncertainty."

Although the film opened at Sundance to mixed reviews, Hendricks's nuanced performance has been lauded (she was "sorely under-utilised", according to one critic). Indeed, Hendricks has such onscreen charisma that whenever she appears in a scene, it is difficult to look at anyone else. The character of Joan in Mad Men started out as little more than a feisty secretary, but as audiences began to respond to Hendricks, the writer Matt Weiner developed her role so that by the end of series seven she had become a complex, fully-rounded character and a linchpin of the entire show.

The same thing happened with Drive, Nicolas Winding Refn's action thriller starring Ryan Gosling as a getaway driver. Hendricks has only a small part as a mysterious woman called Blanche but, according to the Guardian's Peter Bradshaw "almost steals the picture".

Christina Hendricks steals the show as Blanche in Drive. Photograph: Sportsphoto Ltd./Allstar

In person, too, Hendricks is an arresting presence. When she arrives at Joe Allen, her trademark red hair obscured by a straw trilby, the waiters try to make a point of not staring but their mouths drop open anyway, as though their chins have been drawn towards the ground by some curious magnetic force.

Hendricks is in jeans and a black silk top, low-cut enough to reveal glimpses of bra lace. She is swathed in a black scarf, accessorised with a long gold necklace, red lipstick and black eyeliner. The whole thing makes her look like a turn-of-the-century tarot card reader or a beautiful barmaid as depicted by Manet. There is a timelessness to her, a quality of otherness – the legacy, perhaps, of those long-ago schooldays when she refused to conform.

She orders a steak tartare ("I like it spicy") and glass of pinot grigio, and then insists I keep her company by getting a bloody mary. It's 2pm, and I'm working, but Hendricks is impossible to resist. I order the bloody mary.

As we wait for our drinks, I suggest it must be satisfying to look back at those high-school bullies and see how far she has come. She looks at me levelly. "You know, I had so much anger about that time, that experience, for so long and I don't know what dissipated it, but now it's gone. I feel some sadness about it, about how cruel kids can be to each other, but that's it."

She is still friends with three or four people from that period of her life. "But I haven't gone to any reunions." She shrugs. "I'm sure, if I did, they would have no idea I went there. No idea."

It is, you can't help but feel, very much their loss.

When she was growing up, Hendricks never thought of acting as a proper career. She'd been appearing in local theatre productions since the age of nine, along with her older brother, Aaron, and yet, she says: "I know it sounds naive but I didn't know it was a job. I thought it was a hobby."

At the hair salon where she worked as a teenager in Fairfax, the customers kept saying she should be a model. Eventually her mother, Jackie, entered her daughter's photo into a competition to appear on the cover of Seventeen magazine. She didn't win but she got down to the final 10. At 18, she signed with an agency and left Fairfax to live in New York.

She remembers "growing up real fast". In some respects, Hendricks was already used to going it alone. Her parents split up when she was in her much-hated high school – "I always thought they were going to get a divorce," she says now. "I was surprised it took them so long" – and New York gave her a chance to get out of Virginia and away from the locker bay.

She was a successful model, travelling the world and living for a year in London, in a flat just off Holloway Road. Her father, Robert, was born in Birmingham and she has dual nationality, happily describing herself as an Anglophile. "Although," she muses, "I think the beer is stronger there than here. I have two beers in London and I'm, like, wasted."

In her mid-20s, she moved again, this time, with her mother, to Los Angeles. Hendricks was beginning to get a lot of commercial work on television "because I wasn't a typical model. I wasn't 5ft 11in or a beanpole". A manager friend of her brother's liked what he saw and asked to represent her as an actress. Hendricks agreed, on the proviso that she could take acting classes before going up for any auditions. "He was really patient with me," she recalls, taking small mouthfuls of her steak tartare. "So I just started studying. One year later I was watching some movie and I thought, 'I can do that.' So I called him up and said, 'I'm ready.'"

Hendricks got a number of parts in television series, including ER and Without a Trace, but nothing really took off. Then the script for Mad Men came across her desk and immediately she felt it was special.

"I love the idea I have a desk," she giggles now. "It makes me sound very professional."

Both she and her manager wanted her to take the part of Joan. Hendricks's agency didn't agree. "They said, 'It's a period piece, it's never going to go anywhere. We need you to make money and this isn't going to make money.' They ended up dropping me."

Christina Hendricks as Joan Harris in Mad Men. Photograph: Everett Collection/Rex

Hendricks was unruffled.

"I had been on several shows that were meant to be the big ones, that would go on for ever, and they didn't. So there was no sure bet and I'd already taken a chance on them and I felt, why not do the one you're in love with and take a chance on that?"

It was a gamble that paid off spectacularly well. The first season of Mad Men aired in 2007 and was an instant success. Hendricks remembers taking her mother and her best friend to the screening of the pilot episode and being unsure whether audiences would get it. "I turned to them and said, 'Is it good?' And they both said, 'Oh yeah, it's good.' I said, 'Is it boring?' and my mother said, 'No, but I didn't like that he [Don Draper] was cheating on his wife at the end.'"

Hendricks laughs. "And I thought, 'Oh no, she's going to hate the show.'"

After eight years of Joan, Hendricks has just wrapped filming on the series finale. She has several more films in the pipeline and wants to do some theatre – "I want to do everything!" – but Mad Men has seen her through her 30s and saying goodbye has been a wrench. On the last day of filming, the cast gathered to applaud each other as they played out their final scenes and then they hung around "chatting, singing songs, drinking" until eight the following morning. "We all just stuck around," says Hendricks. "We didn't want to leave."

To compound the feeling of uncertainty and change, Hendricks and her hus band have just moved back to New York from LA. "The move has been a really nice distraction," she says. "I don't think it's fully hit me yet… We [the cast] all know each other more than most people on Earth know each other. A lot has happened these eight years. A lot of us have gotten married, bought homes, had children."

Hendricks met her husband in 2007, in the middle of the first season, through their mutual friend, Vincent Kartheiser, who plays Mad Men's Pete Campbell. They married two years later. "So he has been on this journey with me, during which our lives have changed entirely," she says. "He's been amazing. When people are like, 'How are you doing?' [putting on a mock-sympathetic face], he's like, 'She's sad… but she's good.'"

Unlike many of her fellow cast members, Hendricks has decided she does not want children. She had "a million conversations" with Arend about it before they got married and feels very lucky that he agrees. "I mean, they [children] are a lot of work." Has she ever wanted to be a mother? She wrinkles her nose. "I think in my mid-20s I did because I was moving around a lot and didn't have that sense of community, of being rooted."

When she has spoken about this in the past, she has been surprised by the fuss. "Why? I know plenty of people who don't have children. And I also get a lot of people who say, 'Thank you for speaking out, my family don't understand why I don't want kids.'"

Hendricks as Joan with John Slattery as Roger Sterlingin Season 5 of Mad Men. Slattery directs her in God's Pocket. Photograph: Michael Yarish/AMC

Instead, she and Arend have a dog, a beloved cockapoo called Zouzou. Hendricks takes out her phone to show me pictures. She says she had to take a mugshot of Zouzou recently "because she's a service dog and they needed it for her ID".

A what?

"Service dog," Hendricks says again. "So she can travel with me on aeroplanes."

Like a guide dog for the blind?

She nods. "She's an anti-anxiety dog." Hendricks says this totally straight-faced but is that a twinkle in her eye? "She calms me down," she says.

And the air authorities are OK with that?

"You know, they're not legally allowed to ask the reasons," she replies, and then she shows me another photo of Zouzou in a smart green bib that they bought specifically to make her look "more formal".

It's clear that, with Arend and her anti-anxiety dog, Hendricks now has that rootedness she lacked in her 20s, helped also by the firm friendships she established through Mad Men. "I think, with the exception of Robert Morse and John Slattery, none of us were very well known [at the beginning]. We've watched our anonymity being taken away. That's where we are a protective family unit."

The fame is still a strange thing. Hendricks compares the sometimes nerdish preoccupation of Mad Men fans – not unkindly – to the sci-fi community. "They're incredibly passionate," she says, knocking back the last of her wine. "So they always say really kind and nice things."

But she has an issue with the hullabaloo that goes along with being a modern-day celebrity. She dislikes "the lack of respect for someone's privacy" and the way people will suddenly shove a cameraphone in her face without warning. It happened the other night, when she was eating a bowl of spaghetti in a restaurant in London.

"So now – great – there's some horrible pictures of me chewing on meatballs. I've had more people come and say, 'Do you mind if I take a picture because my friend will never believe it.' Really?" she says, exasperated. "Why? Are you just a big liar? That's always the justification or excuse for it because it's not just a picture for them and their friend, it's a picture they're going to put on Facebook for their thousands of friends to look at."

She has a thin skin and hates the constant carping over fashion faux pas or what she perceives as the non-issue of her weight. "I am too emotional," she admits. "I do take things personally because someone is always wanting to criticise or say something negative. I don't know why it is. I'm sure there's tons of blogs out there about how horrible Meryl Streep is." She guffaws at the thought. "And we all know that's not true."

She's right that her physical attributes come up again and again whenever she is interviewed or written about. On one level you can understand why – in a world where wraith-like thinness in actresses is revered, Hendricks is full-blooded proof that gorgeousness can exist, and be embraced, in a different construct. Her costumes in Mad Men – fitted dresses with nipped-in waists and knee-length pencil skirts worn over uncomfortable girdles and underwired long-line bras – only served to accentuate her hourglass figure and have influenced a host of fashion designers.

On another level you can also see why Hendricks is fed up with talking about it, because it is demeaning to suggest that the success of any woman's work depends on her vital statistics rather than her talent.

I've been asked by Hendricks's PR not to ask any questions about her body in the interview. But, obviously, I try to bring it up anyway. Hendricks spots the approach from a mile off. "Don't do it," she says firmly, before I even get to the end of the sentence. She smiles but it's quite clear she means it. She finishes her raw steak and then places her knife and fork together on the plate. Just like Joan, there's a steely underwiring beneath that pale-skinned, blush-cheeked exterior.

Hendricks can more than look after herself. Don't tell anyone, but I'm not sure she needs an anti-anxiety dog after all.

God's Pocket is released on 8 August. The final seven episodes of Mad Men will be shown in 2015

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