Emily Blunt arrives for our interview displaying the sort of sartorial elegance that makes you feel shabby. It’s just after lunch, but you might think she was on her way to Ascot. She's wearing a sleeveless cream dress and turquoise heels, her honey-coloured hair cut to shoulder-length and framing big blue eyes. Her English accent hasn’t dimmed since moving across the pond. This, of course, is something of a sore subject. Last week, Blunt hit the headlines after remarks she made in an interview about becoming an American citizen caused uproar.

For those who missed the story, the 32-year-old – who is married to fellow actor, American-born John Krasinski – recently acquired dual citizenship. It meant taking a written test and even renouncing her Queen – “typically American”, as she put it while appearing on chat show Jimmy Kimmel Live!

“I’m not sure I’m entirely thrilled about it,” she added. “People ask me about the whole day. They were like, ‘Oh, it must have been so emotional.’ I was like, ‘It wasn’t. It was sad.’ I like being British.”

It didn’t help that Blunt had also told The Hollywood Reporter that on the night of her taking the citizenship test, she watched the stomach-churning Republican debate with Donald Trump. “I thought, ‘This was a terrible mistake. What have I done?’” Needless to say, this “off-hand joke”, as she later termed it, apologising for her comments, was taken rather seriously by the more conservative section of the American public. “She has alienated half the country that now will think twice about going to one of her movies,” fumed co-host Steve Doocy on the TV show Fox & Friends.

We meet a few weeks before this storm in a very American teacup. Blunt, to her credit, is not one to hold back. She’s candid about her feelings towards LA, where she and her husband live. “I do have a love-hate relationship with LA because the one industry emanates from every corner of the place, and there’s a certain insecurity that the town is riddled with. If you want to go and find the time to think, LA is not the place. We also have a house in the countryside, which is a much more pleasant place to be.”

You can hardly blame her. She was born in London, the daughter of a barrister and niece of a Conservative MP, so her upbringing must jar with the Californian sunshine. “I miss the pubs,” she says, when I ask what has been hardest to leave behind. “I miss the irreverence, that sense of humour, that way of life, [where] they’re not fussed about much.” Despite being friends with the likes of Anna Hathaway and Amy Adams, it’s been a difficult adjustment.

To be fair, Hollywood has so far welcomed her with open arms. Breaking out as the bitchy assistant to Meryl Streep’s fashion magazine editor in hit comedy The Devil Wears Prada, for which she was nominated for a Golden Globe and a Bafta, Blunt has since worked alongside Matt Damon (The Adjustment Bureau), Bruce Willis (Looper) and Tom Cruise (Edge of Tomorrow). As her husband once told me, “She’s my hero in every single way, in life but also in her career. I think she makes some of the best choices, if not the best choices, I’ve seen.”

It’s been a remarkable rise – made more so by the type of roles she’s getting. Aside from 2009’s The Young Victoria, in which she was marvellous as Britain’s now second longest-serving monarch, she’s rarely been trapped in the confines of the corset drama, like so many British actresses. Rather, she’s been playing tough-as-nails heroines: the gun-wielding mother in Looper; a highly-trained soldier in Edge of Tomorrow; and now, in her new film Sicario, an FBI agent who gets sucked into an off-the-books CIA operation to bring down a Mexican drugs cartel.

While Edge of Tomorrow “was the most physically demanding thing I’ve ever done”, Blunt claims she didn’t set out to take on more masculine parts. “I don’t tend to plan out what I want to do or who I want to be next,” she says. “I have quite a hard time compartmentalising or generalising the kind of people I want to play. So when Edge of Tomorrow came along, I was like, ‘Oh, I haven’t done this before, it’ll be interesting.’ And it really was. It was quite a hard thing to do. I remember feeling a bit restrained by the lack of emotion that this character had.”

What does she mean? “It forces you to not be able to fall back and use any kind of tricks you’ve used before. There’s something rather charmless about the character in Edge of Tomorrow. I remember talking to Meryl Streep when we did Devil Wears Prada, and she said this was her least favourite role, because you’re devoid of any softness or emotion really, and I understand that.” It’s an insight into Blunt, who seasons the best of her work – Sicario included – with just a pinch of vulnerability.

Directed by Denis Villeneuve, Sicario is Blunt’s first role since she gave birth to her and Krasinski’s daughter Hazel, who is now 19 months old. “Denis came to my house when Hazel was five weeks old. I was exhausted, breastfeeding, overweight, and I was just like, ‘Are you sure you want me to do this role?’ It was so not what I was ready for or looking to do.” Did it change her, emotionally, giving birth? “I don’t know,” she muses. “I find it quite hard to specify things that shift you in life. Having a child is obviously one of the more profound shifts.”

Oddly, when Blunt was six months pregnant, she starred in Into The Woods, the recent movie adaptation of Stephen Sondheim’s musical that reunited Blunt with Streep. Playing the baker’s wife, unable to bear a child, it was “the ultimate irony”, she nods. “It was so strange, playing this barren woman. It was good actually for me to be doing something when I was pregnant, and gave me a different understanding of that whole character.” In what way? “Well, what she was yearning for was what I felt lucky to have.”

Blunt does appear to be blessed: the career, the husband, the child – all perfectly in sync. Eleven years in from her game-changing role in My Summer of Love, which saw her win Most Promising Newcomer at the Evening Standard British Film Awards, Blunt hasn’t put a foot wrong, until this recent citizenship misstep. Is it hard to get her head round such success? “Most of the time I don’t think about it, and then occasionally, a night like last night, is quite a strange moment. You’re confronted with this strange person who you don’t really recognise.”

Last night was the Cannes premiere for Sicario, with Blunt looking typically resplendent in a studded Stella McCartney gown. Even now, she looks at the whole circus with an air of detachment. “I don’t ever think whether people know me, or what they think of me … I don’t spend much time thinking about that,” she says. “So when you go through something like that red carpet last night, which is so fantastical …” She pauses, lost for words. “It’s a strange thing.” Perhaps that’s the British DNA in her; as graceful as she looks in front of popping flashbulbs, to be on show is not quite her thing.

Nevertheless, Blunt shines in Sicario in a role that could deservedly see her nominated for the first Oscar of her career. Exploring the increasingly blurred lines between the lawless and those who enforce the law, she plays Kate Macer, an FBI agent who, at the outset, is the leader of a response team that raids a suburban Arizona house belonging to a powerful drugs cartel. Inside it, hidden behind the drywalls, are dozens of slaughtered bodies wrapped in plastic – all victims of the cartel.

Recruited by Josh Brolin’s CIA suit to a special task force operating on the edges of the law, Macer’s heart-of-darkness journey sees her increasingly compromised. “She’s being used. They’re hiding all of their morally questionable acts behind her badge and her integrity,” says Blunt. “I had so much empathy for the fact she couldn’t use any of her previous training that she was incredibly competent at. None of it was allowed to be used in this incoherent world, so her ideals are being torn apart, and by the end of the movie she’s sort of a shell of her former self. In just three days how quickly things change.”

Drawing comparisons to both the Oscar-winning drugs drama Traffic and the hunt-for-Bin-Laden tale Zero Dark Thirty, Blunt makes one thing clear: “Although it’s very violent and very dark, it’s not gratuitous.”

When it came to the research, living in California, Blunt was already up to speed on the war on drugs. “It’s a more prominent issue there. But I learned much more about it speaking to Taylor [Sheridan, the screenwriter]; the script was very informative. Also, you just go online and look up the history of these cartels … [They're] very brutal.”

She also spoke to real-life FBI agents. “They sound like normal girls. They go home and watch Downton Abbey. They’re great girls. You definitely want to have a beer with them. I found that interesting – to get under the skin of what it is to be a female cop and what that costs you; how it affects your marriage, how it affects how you sleep at night, how you cope with the men working alongside you. It’s really interesting, hearing their point of view, and quite humbling.”

Shooting in Texas just four months after giving birth was a gruelling experience – both physically and emotionally. “There were days where I felt as frustrated as the character,” she admits. “It’s a film that can really get under your skin, and the experience of shooting some of the scenes was quite unnerving actually.” How much did she take home with her? “Certain scenes I had a bit of trouble sleeping afterwards,” she nods, “but I have a baby now.”

Unsurprisingly, given the way Hollywood works, there was a moment in the life-cycle of the film’s long-gestating production when the writer was told to turn the Macer character into a man. Thankfully, he refused. Did that affect Blunt’s performance when she found out? “I wasn’t really aware or thinking about adjusting to make it more masculine,” she answers. “She’s definitely trying to survive in a predominantly male-driven industry or profession.”

The same could be said for Blunt, although she finds the endless debate about the sexual politics of Hollywood "nauseating". “I’ve been doing this for 14 years, so I feel much more valued within the industry than I used to. But I think that’s the case for men as well. The industry is not your friend, you cannot trust it, it’s not your pal … It’s a very precarious job. But I think sometimes I feel we can exacerbate the problem of the divide between genders by talking about it too much and not doing enough.”

When it comes to the man in her life, there’s no such divide. There probably isn’t a more united couple in Hollywood. Blunt started dating Krasinski, best known for playing Jim in the American version of The Office, in 2008. Their first date was at a gun range, so sure was he that she’d soon be seeing another man. But they married two years later; and, yes, she admits being with an actor is an advantage. “We talk about everything,” she says. “To have someone who is in the industry and understands it as well as I do is a huge comfort.”

The second of four children, Blunt is not the only one in her family to be married to an actor. Her sister Felicity, a literary agent, is wed to Stanley Tucci, Blunt’s co-star from The Devil Wears Prada. But growing up, life was different. Her mother Janice may have been a former actor, but with her father Oliver a criminal defence lawyer (and her uncle, Crispin Blunt, the Conservative MP for Reigate), Blunt’s childhood was hardly steeped in the entertainment industry.

Her introduction to acting came when she suffered a youthful stammer which gradually receded as she took on roles. “I honestly didn’t think I wanted to be an actress until someone saw me in a school play,” she says. “I was not ambitious in the slightest. I enjoyed it. I enjoyed doing it at school. And then I did a play at the Edinburgh Festival Theatre [a student production of a rock musical called Bliss]. I was 17, and an agent came to see it, and he said, ‘Do you want to do this? I think you could do this.’ I was a bit surprised.”

Even then, Blunt was not convinced. She was planning to study modern languages. “I’ve always loved speaking Spanish and French, so I was going to be a translator [for the UN],” she says. “I remember that last week at school, filling out whether you went to drama school or university, and I was going to go to university.” But after her Edinburgh experience she took a different path. By the time she was 18, she was acting in London’s West End, opposite Dame Judi Dench, in a production of The Royal Family.

She followed it with sundry TV appearances, in shows like Foyle’s War and Poirot, before she landed 2004’s coming-of-age drama My Summer of Love, in which she played a middle-class girl embroiled in a lesbian love affair. “I think I’ve brought elements of that experience to every other job I’ve ever done: making changes, offering suggestions, having a responsibility to the story, and propelling the story forward. I don’t ever want to be a lazy actor, and not ask questions and not offer a solution or a change.”

It’s been a whirlwind ever since. She dated Canadian singer Michael Buble for three years, won a Golden Globe for her performance in Gideon’s Daughter, playing the troubled offspring of a New Labour spin doctor, and became an ambassador for the Yves Saint Laurent perfume Opium. There’s an effortless elegance to her, particularly when it comes to fashion, though she doesn’t take it too seriously. “I quite like the spectacle of it all, I think it’s quite good fun.”

She’s next up in The Huntsman, the sequel-of-sorts to Snow White and the Huntsman, which will see Blunt play “a villain” – Freya, the Ice Queen, sister to Charlize Theron’s insane Ravenna from the original. She’s also attached to The Girl on the Train, a thriller based on the hugely popular novel by Paula Hawkins about a woman who becomes entangled in a murder investigation. But decisions are harder now, with a baby to look after. “It has to be worth it,” she says. “You really have to decide what project is worth that commitment and time away.” Maybe some time out of America is what she needs right now.

Sicario (cert tbc) opens in cinemas on Friday.