Petite and pretty, Olsen is instantly recognisable when she arrives, wearing gym clothes – an exercise top, leggings and black trainers – with her blond hair scraped back into a messy ponytail and a chic bag from The Row, one of her sisters’ fashion labels, over her shoulder.

Down-to-earth and self-deprecating, she is seen as the most “normal” of the Olsen sisters, apparently unscathed by the media circus that has surrounded her family since Mary-Kate and Ashley made their acting debut, aged only nine months, on the American sitcom Full House. “It’s just crazy,” says Olsen, 26, who is three years younger than them. “They’ve never had a year off work their whole lives.”

In recent years the twins have distanced themselves from the film industry, focusing on their work as fashion designers. “They’re amazing, diligent, kind, beautiful, hard-working women who have tons of responsibility and are great at what they do,” Olsen says.

In the meantime Elizabeth – or Lizzie, as she is known – has gently manoeuvred herself into the limelight. In 2011 she caused a sensation at the Sundance Film Festival with her beautifully nuanced performances in two independent films: Silent House, an American remake of a Uruguayan horror film; and the critically acclaimed drama Martha Marcy May Marlene, in which she played a girl who escapes a dangerous cult.

Since then she has delivered equally deft performances in several less memorable movies (Liberal Arts and Red Lights, for example), but she reached a much wider audience with last year’s Godzilla remake, in which she played a young nurse and mother married to a military bomb-disposal expert, the film’s hero, played by Aaron Taylor-Johnson. She reunites with Taylor-Johnson in Avengers: Age of Ultron, this time taking the role of his twin sister, Wanda Maximoff, aka the Scarlet Witch, while he plays the superhero Quicksilver, also known as Pietro Maximoff.

The fourth of the Olsen siblings (there is an older brother, James), Elizabeth was born in Sherman Oaks, a Los Angeles suburb, to Jarnette, a former dancer, and David, a property developer. Contrary to popular perception, they were not pushy stage parents. In fact, they stumbled into the industry when a friend’s child’s agent mentioned they were looking for twins to share a role in a new sitcom. “My parents didn’t know much about the industry, so they just surrounded themselves with people who did,” Olsen says.

They divorced when Olsen was very young, but she is close to both parents and says that her father often visits her on set. “But I wouldn’t let him come [on] Martha Marcy May Marlene. I was raped and naked in that movie. He did end up seeing it with me but I could nudge him so he knew when to close his eyes.”

Olsen says she has always been a huge fan of the comic-book-superhero genre. “Iron Man was mind-blowing to me, that was the first of them.” And as a little girl, she says, “You couldn’t pull me away from Star Wars and The Lord of the Rings. Guillermo del Toro? Love. Return to Oz? Love. I love anything that is weird, big and creepy.”

Letting it be known that she was in the market for blockbusters, not only independent films, Olsen had two meetings with the Marvel team, then met with Joss Whedon, the Avengers director. “I didn’t even know what the role was because they’re so mum about everything.”

The new film focuses on the superhero Iron Man, played by Robert Downey Jr, who tries to re-energise a dormant peacekeeping programme. Naturally, things go wrong and it is up to him and the other Avengers – including Thor (Chris Hemsworth), the Black Widow (Scarlett Johansson), Captain America (Chris Evans), Hawkeye (Jeremy Renner) and the Hulk (Mark Ruffalo) – to stop the supervillain Ultron (James Spader) from enacting his evil plan to wipe out the human race. Along the way they encounter mysterious twins with special powers, Pietro and Wanda Maximoff.

One of the first people she called when she was finally offered the part of the Scarlet Witch was Taylor-Johnson. “Aaron and I had just finished working with each other and we both got roles, so we were like, ‘Are you going to do it?’ ‘Are you going to do it?’ ‘Let’s do it.’ It was awesome working with him a second time. I love him and his wife, Sam [Taylor-Johnson, who directed Fifty Shades of Grey], and spent lots of time with them when we were shooting in London.”

As for the rest of the cast, Olsen says – predictably – that they all got on well. “Everyone was incredibly kind and playful. Paul Bettany [the Vision] is hilarious, Downey’s the kindest, Renner is a really funny person. I didn’t spend much time with Scarlett because they filmed her separately when she was pregnant. Ruffalo, Chris Evans, Hemsworth – they’re all so nice. We had one dinner as a gang but everyone had moved their families over to London [for filming] so they didn’t want to hang out with me!”

She describes her on-screen character as unusual in the Marvel universe. “A lot of the characters have a snarky humour, but she’s not that person. She has a different energy among the group. She has telekinetic powers and can manipulate objects and minds. What I loved about her is that she feels everything deeply, as if she’s in someone’s head. She doesn’t just understand their thoughts, she goes through their feelings: the ultimate empathy. She’s an incredibly sensitive person and I loved having the dynamic with Aaron, who is my agitated, impatient brother. She grounds him.”

Olsen herself sounds grounded too. “I don’t have a crazy life. There’s nothing that exciting about me. I don’t have many people I date…”She recently broke up with her fiancé, the actor Boyd Holbrook, whom she met in 2012 on the set of Very Good Girls. “That was as serious as it gets,” she says of the relationship, adding that its end has not put her off the idea of marriage and children. “There’s nothing weird, I think, about getting married. And having children is a beautiful, amazing thing.”

A recent article cited Olsen and Shailene Woodley as examples of how disconcertingly well adjusted the latest crop of Hollywood actresses are, appearing to lead clean, drug-free lives untainted by the whiff of scandal. “It’s a trend to be mindful in a way,” Olsen agrees. “Actresses used to be crazy beautiful people living terrifying lives.” Referring to the celebrity-photograph-hacking scandal of last year, she adds that there would be nothing sensational if she ever fell victim to something similar. “If anyone ever hacked my computer or iPad, all they would find would be videos of me singing in my car – I lip-synch and send the videos to my friends.”

She says that she has never been tempted to rebel, not even as a teenager. “I tried smoking but it made me feel horrible. I’m not a rebellious person by nature. I do drink wine – I love food and wine, I can’t have one without the other.”

Today she is drinking a spinach, kale, celery and hemp-seed smoothie – with an extra Vitamineral Green shot. But she grimaces after she takes her first sip. “There’s salt in it,” she says, shocked. “I would never put salt in a smoothie.” Nevertheless, she won’t even contemplate sending it back. “I’m not that person, I can never send anything back.” She adds that until recently she would never complain about anything and always took the blame if things went wrong. “I think I’m getting better at that with age.

But then the other day I was at a photoshoot and something wasn’t working – I don’t know whether it was the clothes or the hair or the lighting – but instead of just saying, ‘Why don’t we try something new?’ I said, ‘I’m sorry, I’m really insecure today.’ Even though I wasn’t. I do realise there are other ways to go about saying something than throwing yourself under the bus and making yourself feel like an idiot, just so no one else feels bad.”

In the past Olsen has said that she thinks she is a 50-50 combination of both of her sisters. “I don’t know if that’s still accurate,” she tells me now. “But I do think they are very different from each other. In my mind they’re completely individualised.” Although she loved acting as a child – and even had a cameo, aged five, in her sisters’ film How the West Was Fun – she tried to suppress that as she got older. “I thought, ‘Everyone in LA wants to be an actor, that’s such a cliché, I want a business, I’m going to be an accountant.’”

A diligent student, she says she was never satisfied with anything less than an A-plus. “I was like a crazy person – if my math teacher gave me a 97 instead of a 98 [which qualifies as an A-plus], I would argue with him to get that extra point. My dad still makes a joke about it today – he’s like, ‘Lizzie, you could have been on Wall Street.’” But she didn’t want “a life based around money”, so after school she returned to acting, opting for theatre rather than films because she felt that was a less obvious route and somehow more worthy.

She moved to New York to study drama at the Tisch School of the Arts, and also worked as an understudy. “I always did my own thing. I had no social life,” she says. Her breakthrough came when she met the writer and director Sean Durkin, who was looking for an unknown actor to star in his debut feature-length film, Martha Marcy May Marlene. “It was like a really big gift. I learnt a lot quickly, and Sean has since become one of my closest friends.”

Over the years Olsen has, she says, become more selective about roles. “When I first started working, I was so excited that people wanted me that I said yes to anything. I wasn’t making any conscious choices at all.” She recently finished shooting a Hank Williams biopic, I Saw the Light – directed by Marc Abraham and starring Tom Hiddleston as Williams – in which she plays the singer’s wife Audrey Mae. The film focuses on the years leading up to his death at the age of 29. “It’s certainly not a comedy,” she says with a wry laugh.

Unlike most actresses, she looks forward to getting older, she says. “I believe that roles get better for women in their thirties and forties. I’m 26 but I look 21. I can’t play a 30-year-old, but I also can’t play a teenager because it’s completely unrelatable to me now.” These days she feels much more settled. “I don’t have that anxiousness. I have enough confidence in my work ethic and hopefully a good enough reputation that I don’t think [my career] is going to disappear at any moment.” Perhaps thinking that sounds a little too complacent, she adds hastily, “Although I definitely don’t feel I’ve arrived as such. Not yet.”