“Man, I’m terrified of young ­actors,” says Rose Byrne. “They’re so confident, they’re so self-possessed, they’ve got a brand and an Instagram handle and a TikTok channel…” The 43-year-old takes a breath. “I’m like, ‘Can you help me figure out what I’m supposed to do?’ They’re running the world. I’ve never been more intimidated.”

I suspect people felt the same about Byrne once. I’ve seen pictures of her and Heath Ledger – a pre-stardom photoshoot they did to promote the 1999 comedy crime caper Two Hands. Back then they were fresh-faced 20-year-olds just off the plane from Australia – on the cusp of fame, on the cusp of the millennium – gurning at the cameras on Hollywood Boulevard, looking effortlessly cool. To older actors, they probably looked like they were running the world too.

“Maybe,” says Byrne, unconvinced. “I don’t think so with me. I definitely never had that innate self-possession. I meet young actors now and I’m just like, ‘If I had an inch of your confidence at that age, I would’ve been a different person.’”

It did take her a little longer than Ledger to find her footing. While he quickly became both a heartthrob and an Oscar nominee, it would be another decade before Byrne hit the mainstream. In the Noughties, she had small roles in big films, like Star Wars: Episode II – Attack of the Clones (as Natalie Portman’s handmaiden), Troy and 28 Weeks Later, but she was far from a household name. Then, in 2011, Bridesmaids came along. One of the best comedies of the 21st century, in which she played the pristine, uptight foil to Kristen Wiig’s chaotic lead, it made her a star.

After that came X-Men: First Class alongside James McAvoy, Michael Fassbender and Jennifer Lawrence, Spy with Melissa McCarthy and Bad Neighbours with Seth Rogen. There were prestige television roles, too, in shows such as Mrs America – in which she nailed feminist organiser Gloria Steinem’s cool, righteous reserve – and Physical, the dark comedy in which she plays a bulimic aerobics pioneer. She is shooting season three of that show now in LA (she is late for our phone call, in fact, because today’s shoot overran). You could say that her speciality is women with that innate self-possession she insists she never had.

Her latest role, though, doesn’t fit that bill. Seriously Red, which stars Byrne’s old school friend Krew Boylan, who also wrote the script, follows a flailing screw-up called Red who is fired from her day job and becomes a Dolly Parton impersonator. In the process, she finds, loses and then finds herself again. Byrne has a small but unignorable role as a disgruntled Elvis impersonator.

It is a curious film, charming in its way. Some jokes hit the mark, others misfire – there is one about Red sexually harassing her colleagues that includes the line “hashtag me too – too many crotches”. But it has some worthwhile things to say about the nature of identity. “Dolly Parton is about being the best version of yourself,” says Red’s best friend at one point, “but you’re living as someone else.”

When Byrne read the script, “I just thought it was unique, very funny, very bittersweet, and like nothing I’d ever read,” she says. And what about her own character? We never meet them out of their costume – they are credited simply as EP – or learn anything about them except that they have a propensity for cruelty; in one key scene, they make disparaging remarks about Red’s body.

“They are an antagonist in a way,” says Byrne. “They are kind of a villain and also a tragedy. I very much wanted to remain unknown, a mystery. This shadiness is important for Red’s story – for those memories when someone really shatters our illusions, or shatters our perceptions of ourselves, or makes a cutting remark that we can never recover from.”

Why Elvis? “Krew took a look at me one day, and was like, ‘You look like him. You have the same shape face.’” I wonder whether that’s a compliment. “Absolutely!” says Byrne. “Are you kidding me? He was one of the most beautiful men, oh my goodness.”

When it came to preparing for the role, it helped that Byrne’s husband – the actor Bobby Cannavale, who recently starred in Nine Perfect Strangers and the controversial Marilyn Monroe film Blonde, and with whom she has two young children – is a huge Elvis fan. “He just finished reading the seminal Elvis biography Last Train to Memphis, and he’d read passages out to me,” she says. She would watch hours of footage, too, though she wasn’t quite as dedicated as some of the extras, who were real-life impersonators. “The guy who played Diana [Princess of Wales] never broke character on set, ever,” she says. “It was like working with Method actors.”

Byrne has never been the Method type – though she has no trouble embodying the roles she plays. She thinks it is because she is not particularly distinctive – or so she said in a recent interview, which I read back to her now: “I don’t think people ­really associate me with anything except for maybe a general familiarity. It means I can vanish into parts, but this is a business too. People want that instant hit, that instant gratification…”

“Oh God, this is the worst,” she says suddenly, with a slightly frenzied laugh. “You’re going to read back my quotes?! Are you trying to kill me?”

It’s an interesting quote! “Oh my God. I’m going to jump off a bridge. Oh God. Can you read someone else’s quotes? Another actor?”

I can actually. “OK, I’d prefer that.”

Saoirse Ronan was talking about Bridesmaids a few years ago, and…

“Oh, you’re really going to do it?”

Yes. “Right!”

Saoirse Ronan was talking about Bridesmaids a few years ago, and how she recommended the film to a male friend who had never seen it. His response? “It’s just a film about girls, isn’t it? Just a bunch of girls.”

“I was so upset,” said Ronan, who was promoting Greta Gerwig’s masterpiece Lady Bird at the time, “that there is this perception of a female film being something lesser than what you would have with a group of men.”

“Thanks, Saoirse!” says Byrne brightly. Did she experience anything similar when she was promoting the film, or even in the years since? “At the time I did, and I was so naive. I did not think that I would be talking about it. [Bridesmaids] was definitely unusual. ‘I get to work with all these actresses? That never happens!’ But I had no idea it would become such a pointed discussion. I’m a different generation to Saoirse, so I don’t know what a 20-year-old would think of that film now. I would think it wouldn’t be that big of a deal – that it wouldn’t be commented on, the gender of it.” She pauses. “But we’re all in pink dresses on the poster, so that was enough to scare him off.”

It still exists, she adds, “that preconceived idea about what can be funny and what can’t”.

Byrne didn’t realise she could be funny. When she filmed ­Bridesmaids, she was intimidated by the comedy heavyweights she was working with – Wiig especially, who she had loved for years. It took a while for her to relax, to be confident that she had been cast for a reason. As you may have gathered, it is not in her nature to be particularly self-confident.

“You’d think a performer would be an extrovert, but it makes sense that they can also be quite shy,” she says. “When you’re performing, you are allowed to do whatever you like. I’m probably less shy now, but I definitely did fall into that category.”

Byrne has been acting professionally since she was 15, when she would do theatre in her hometown of Sydney. “You want to hide behind the performance, rather than show your personality. An old friend once said to me: ‘There are two types of actors: ones that want to be seen, and ones that want to be hidden.’” And is she in the latter camp? “I guess I’m more interested in trying to change, rather than just fall back on something that I know in my own life.”

She must find it hard, sometimes, to shake off the characters she plays. “Look, when you’ve got two little kids, they just don’t have any patience for any of that,” she says. “Even if I do, they have no patience for any kind of navel-gazing.”

Maybe they get that from her.

Seriously Red is out now