When Christina Hendricks walks into the restaurant on Sunset Boulevard in a crisp white top, red cropped trousers and black flats, laden with shopping bags full of homewares for the new place she and her husband have just moved into nearby, she looks so much like a young starlet from the 50s that it's hard not to wonder if she arrived in a DeLorean. (In fact, at the end of the interview she is picked up in a decidedly unsci-fi olive green Chevrolet by her husband, the actor Geoffrey Arend, whose gangly profile and mess of curly hair are just visible in the front seat.)

Even without the 60s pencil skirts and beehive do that her character, Joan Holloway, currently models in Mad Men, Hendricks, 36, looks like something from a different age who has somehow landed in the modern day. This is not, I should add, a veiled reference to her frankly over-discussed figure. Since Mad Men began in 2007, some critics have been so busy noting how we live in an era so different from the sexist workplace of Sterling Cooper – in which women's bodies are lustily discussed in front of them – that they have apparently not noticed they often do the same thing with actors, especially Hendricks. It's hard to think of another female star whose body has come under so much scrutiny of late. While most of the attention has been positive, there is a thin line between celebrating someone's appearance and reducing that person to nothing more than her physique. And this would be unfair to Hendricks because her performance as Joan is very subtle, lifting the character beyond camp and vamp.

And anyway, Hendricks' retro quality is not simply due to her womanly shape. It's also down to her ramrod deportment – probably a hangover from her teenage years spent doing ballet – and her voice, which is more Marilyn Monroe-ishly girlish than it is as Joan, rising to high-pitched babyish when she talks about Arend ("I am kinda crazy about him," she concedes, when she catches herself smiling when his name flashes up on her phone). Her walk is pure Joan sashay.

"Yeah, my husband says, 'What Joan walk? You've always walked that way!'" She laughs.

Her old-school look makes her a canny bit of casting in her new film, Drive, about a stuntman, played by Ryan Gosling, who works occasionally as a getaway driver, a part-time job that ploughs him into a heap of trouble. Part of that heap is Hendricks who, even though the film is set in the present day, plays a double-crossing femme fatale named Blanche.

She says she took the job because she wanted to work with the director, Nicolas Refn Winding, who directed Bronson and Pusher, and he has since returned the compliment by saying he would love to cast her as the eponymous heroine in his possible next film, Wonder Woman. Would she do it?

"Absolutely!" she says, her big blue eyes widening in astonishment that the question even has to be asked.

Aside from the aesthetics, there is a level-headedness to Hendricks and a lack of interest in celebrity that seem anachronistic in Hollywood today. Even when she was working as a model in her early 20s, she maintained a cool self-possession reminiscent of Joan's approach to her secretarial colleagues. She started modelling after school when she won a contest in a magazine: "But I didn't do it because I wanted to be a model – I did it because I wanted to get out of Virginia," she says emphatically.

She wasn't friends with most of her fellow models. "I met a lot of young girls modelling and they were like, 'Oh, I'm running around town and people are taking my picture', while I was saving receipts and learning how to be self-employed," she recalls with just a lick of scorn. When she was given an invitation to Johnny Depp's birthday party, she sold it for groceries. "I was astounded I was invited because I didn't know him. When someone said, 'Well, the organisers want pretty models there,' I said, 'Well, that doesn't seem appropriate!' So I sold it," she says stoutly.

Hendricks worked as a model from the age of 18 to 27, and during this time fulfilled a long-held dream and lived for a year in London, just off Holloway Road: her father was born in England and she has dual nationality. "I loved it," she says. "And it was only then that I began to understand those kind of off things my dad does, like put butter on sandwiches. I was like, ohhhh – that's an English thing!"

Her pragmatic approach to modelling stood her in good stead when her agent told the UK-size eight 25-year-old to lose weight. "I thought, well, you might see curves there, but that's just a bone" – she punches her right hip, hard – "so even if I lose weight that's not going to change anything. That's how I look. That's my shape. Do the math." She shrugs and reaches for her glass of white wine. She didn't lose any weight.

Where did such maturity come from? "From growing up in a little town in Idaho. We were probably the last people in the country to get a VCR and we didn't have cable. There wasn't any admiration of glamour, no, 'I want to look like them or have that lifestyle', because everyone in my town had the same lifestyle. So I didn't think, 'Ooh, a movie star's birthday!' I just thought, 'What?'"

Hendricks has always trusted herself instead of the crowd, a habit that has worked out more happily for her as an adult than as a teenager. While she was a good student, she was also "pretty unhappy. I wouldn't say I liked school – ever." She, her older brother and parents moved from the small town of Twin Falls, Idaho, to the larger one of Fairfax, Virginia, just before she started high school: "And moving as a teenager is never easy," she says drily. She was "a goth kid – I dyed my hair about 42 different colours, and kids can be pretty judgmental about people who are different. But instead of breaking down and conforming, I stood firm. That is also probably why I was unhappy."

"Standing firm" worked out better 15 years later when she saw the script for Mad Men and her agency refused to let her take the part. She had been living and working in LA for a few years and had a recurring role on ER, but nothing had really taken off yet. "They said to me, 'AMC [Mad Men's network] doesn't have any other big shows – why would you do this instead of taking something that's a better bet?' I said, 'Look, I've gone with the one that's the better bet in the past – let's go with the really good script this time.'"

So she took the role. Her agency dropped her. She shrugged and found herself a new agency.

Since Mad Men achieved such enormous success, Hendricks has had to learn how to stand firmer than ever. She has come under intense scrutiny from the press, her body and fashion choices dissected. "It just seemed so odd as people had never commented on my body before. Every woman obsesses over her figure, but I was happy, I felt sexy – I never thought about it. I know this sounds naive, but I honestly never expected this kind of attention."

A particularly cruel critique came from Cathy Horyn, fashion editor of the New York Times, in January 2010 in her article about the Golden Globes, in which she referred to "Christina Hendricks in Christian Siriano's exploding ruffle dress. (As one stylist said, 'You don't put a big girl in a big dress. That's rule number one.')" The paper also distorted the photo of Hendricks on the page, making her look wider, for which it later apologised.

"It was rude. I know she was just doing her job but it was goofy and it hurt my feelings," Hendricks says, wincing at the memory.

And hadn't she just come back from her honeymoon? "That's the thing!" she bursts out. "I'd just come back and was so happy. And she said that mean thing and I was like…" She scrunches her face up. "If you look at me one week later at the Screen Actors Guild awards, I look like this" – she makes a sad face – "because I'm like, please don't say anything mean to me." She gives a little self-mocking laugh.

Hendricks met Arend in 2007 through their mutual friend Vincent Kartheiser, who plays Pete Campbell on Mad Men. "Geoffrey came in with this sexy curly hair and he had his tie in his hand and his shirt was buttoned wrong, and I thought, oh he's cuuuute," she says, wiggling in her seat with pleasure. They managed to stay just friends for a month, "then he kissed me", she sing-songs. They got married in 2009.

The day after we meet, Hendricks will begin shooting the next series of Mad Men. She has been playing Joan for so long now – and will continue to play her for another three series, it was recently announced. How would she like Joan to end up? Hendricks smiles and glances down at her own wedding ring: "Happy! Happy and in love. That's all."

Has the scrutiny the role has brought made her more self-conscious? "There is an element of that, yes. Some of the things people have said about me, well, they're unbelievable." There have been more flattering accolades, too, with various men's magazines all keen to name her the sexiest woman who ever drew breath. "It's very nice but my husband always says, 'I told you that years ago!'" she says with a real smile. "He's the one who makes me feel sexy."

• Drive is released in the UK on 23 September