n a raging storm in the Peak District last winter, a blue Toyota Yaris was parked in a remote roadside spot with a sex scene being filmed inside it. "It can pose challenges, depending on the size of the car," chuckles Romola Garai. "Me and Dominic [Cooper] got in this hatchback and asked: 'How far do these seats go back?' Soon there was a gale blowing outside. We were in the car, ready to shoot, but outside the entire film crew were being buffeted by high winds. They said: 'You guys stay in there, don't get out!' while all the lights were getting blown away."

What did the co-stars do while the camera crew battled the elements? "What actors always do in these situations – have a long, gossipy conversation about people in the industry. While everyone else was trying to save the show, we were sitting in the car, like: 'Well, I've heard he's a total nightmare!'"

The in-car tryst is a pivotal moment in new drama Adultery, created by Bafta-winning writer Danny Brocklehurst (Shameless, Fool Me Once, Brassic). The six-parter is billed as a "steamy, scandalous romance" about a whirlwind fling that threatens to unravel two families. Personal trainer Beth (Garai) and GP Tom (Cooper), both married, are thrown together when their teenage children start dating. Insatiably drawn to one another, the pair embark on an intense illicit affair.

Can they keep it secret? Will the guilt get too much? Might they even leave their respective spouses? There are shades of Doctor Foster, Cold Feet and The Affair as the story unfolds. The 44-year-old actor – who helpfully explains that her name is pronounced "Romola with the emphasis on 'Rom', not 'ola', and Gary as in Neville or Barlow" – admits the premise gave her pause.

"I picked up a script about a cheating wife, written by a man, with a little bit of hesitation," she admits. "In our cultural imagination, unfaithful women haven't always been well served and can often be a projection of male insecurity – from Eve onwards. But some of my favourite books, like Madame Bovary, are so much more than that. Happily, Danny's scripts were brilliant. They go into the complex area of marital disappointment. Beth's dissatisfaction isn't based on anything big. Her husband is a good guy but she's had to suppress herself. By the time Beth realises she's given up too much for her marriage, it's too late. When you have an extreme physical connection with someone else, growing in the fertile ground of marital disappointment, disaster ensues."

Garai immediately connected to the character of Beth. "I just knew her. There are so many versions of that woman in my life. Somebody who's exhausted from doing all the right things. Ferrying the kids around, washing the team's football kit, contributing financially to the home in two different jobs. She's part of the sandwich generation and she's overwhelmed. I was like: hard-relate. No acting required. She's also had to give up her own business. I know so many women who had high-powered jobs which went on the back-burner in service of the family. It gave them meaning in their life and value in society. Losing that can be destructive. Resentment sits inside you like a little gremlin."

Extramarital liaisons take place in cars, kitchens and toilets – not to mention the storeroom of a city farm. "I'll never look at a city farm the same way," says Garai. "As a mother of two [she's married to actor-director Sam Hoare and they have two children, aged 10 and 13], I've spent many a day at those places but certainly never had anything like that happen. I just had a juice box and bought a squirrel keyring."

Sex scenes have transformed since Garai started out. "They never used to be properly directed," she says. "It was a case of 'Do what you want. As long as she gets her tits out, it doesn't matter.' Which was awful for 90% of people and great for 10% of people. It's so much better now with intimacy coordinators. There are respectful, technical conversations. You're doing it like a stunt, basically, with the equivalent of a fight director telling everyone exactly what to do. You have a very strong line of communication with someone whose responsibility, apart from getting the footage, is to ensure you feel comfortable. It's a shame it had to get so bad before change came."

Humour helps, too. "Sex scenes are still weird and a bit embarrassing. Physical intimacy with another person releases all sorts of chemicals. Your body is responding and your brain sometimes doesn't know how to process that. So it's useful to have a scene partner you can laugh with. It releases the tension."

Garai gets a Meg Ryan moment as the camera lingers on her orgasmic face. "Our intimacy director asked: 'What's the storytelling here?' And I was like: 'Well, I think she comes.' Beth is sexually unfulfilled in her marriage. It was important to see her get the specific thing she's lacking in her life: sexual pleasure." She laughs. "All it's missing is a woman in a diner saying: 'I'll have what she's having.' Hopefully the audience will fill in that gap!"

She realises adultery is a hot-button topic. "I've already had some pretty punchy conversations, just by telling people what the show's about. At the hairdresser's or school gates, I'll say it's two ordinary married people who have an affair and people are angry already. Cheating is an issue that's affected or wounded everyone." Will there be whispering in the street? "Hope so," she grins. "I have such a boring life, I love the idea of causing scandalous chat. Maybe I'll become a figurehead for adulterers. Women might come up and say: 'Now you understand why I was serially unfaithful to Jasper!' I'll be like: 'I really don't! Poor Jasper!'"

Adultery doesn't flinch from the fallout from the affair. "It doesn't pull its punches," says Garai. "I'm like a prefect on set and thought it was important to show the impact on their spouses and children." How is she a prefect? "You know in Celebrity Traitors where Professor Hannah Fry says she's dripping with prefect energy? I've got a similar vibe, albeit for less academic reasons. I like to talk about the moral aspects of scenes more than other actors. I don't mean that as a boast. It's probably deeply annoying. I bet Danny would be delighted if he never saw my face looming at him again!"

She also points out the double standard of how men and women are judged for affairs: "Women get called 'whores'. There's no slur word for sexual incontinence in men. You'd never call a dude a 'home-wrecker' either." Even the show's title caused misunderstandings. "People would ask my kids: 'Where's Mummy? She's not been around for ages.' They'd reply, 'She in Manchester doing Adultery. She's busy with Adultery."

Could Garai's husband and Cooper's partner, Gemma Chan, start looking at them askance? "I knew you'd ask that!" she says. "Thankfully not, because there's nothing more helpful for the stresses and strains of a marriage in midlife than doing a show like this. It really makes you discuss the pitfalls. I hope it provokes conversations between couples at home. Beth and Tom are both the hands-on parent. They're the carers. But it's them that have the forbidden relationship. They're good people doing something bad."

Garai had to master a Manchester accent for the part. "That was terrifying," she says. "I tried to stay in it on set, which makes everyone call you a twat. People took the piss but I went through fire to make it as accurate as I could. When the show airs, I'll stay away from Mancunians because I'm sure they'll tell me exactly what they think!"

Equally challenging was leading a zumba class. "What got me through the embarrassment was the sense of a woman who loves being in her body. Beth relishes being sweaty and having that endorphin release. It relates to her quest for passion. There's a well-spring of physical energy within her which needs to be run off. She wants to feel alive and feel joy." She also croons loudly along to the car stereo. "That was another moment with heavy cringe factor. I figured that Beth married too young. Singing and dancing shows her longing for lost youth. For freedom, for fun, for sex. But belting out Rhythm Is a Dancer without a backing track? God! Dominic and I were both like: 'Let's never speak of this again.'"

Much of Adultery's intrigue is played out via technology. Sexy selfies are sent, phone-tracking apps are deployed, Insta accounts are stalked. Teens are regularly told off for being glued to their devices. "Of course, it's all bullshit," says Garai. "Kids would be perfectly within their rights to say: 'No, fuck off, older people. You're all on email for work, you're meeting people on Hinge, you've got Ring doorbells for your parcels.' The show attacks that hypocrisy. Technology is ingrained in all their lives. Personally, I'm a complete technophobe with very mixed feelings about social media but it's a huge part of modern relationships."

Garai was among the 80-plus women who accused Harvey Weinstein of sexual misconduct in 2017, allegations that sparked the #MeToo movement. Has enough progress been made? "It's much harder for women to get sexually assaulted at work now, which can only be a good thing. Social media played a huge role. It gave women the power to push back against systemic abuse. They could call it out anonymously and en masse. I'm happy but also sad it wouldn't have happened without social media. The tech itself is something I'm still conflicted about."

Garai has been a reliably excellent presence on stage and screen for two decades. Her TV breakthrough came in 2011 when she was Bafta-nominated for playing a polymath sex worker in The Crimson Petal and the White. She got a Golden Globe nod the following year for period newsroom drama The Hour. Other TV roles include Emma, Born to Kill, The Miniaturist, Just Act Normal, Scoop, Betrayal and Vigil. Such roles have been punctuated by acclaimed theatre work.

She won an Olivier award last year for her blistering performance in the stage adaptation of Annie Ernaux's memoir The Years. Garai was actually nominated twice, for her back-to-back performances in The Years and Giant, the play about the antisemitism row that engulfed Roald Dahl. This double honour led to the strange sight of Garai competing with herself, simultaneously appearing in two closeups as the winner was announced. "That was so surreal," she smiles. When her Giant co-star John Lithgow collected the best actor gong, he began his acceptance speech with "Romola, I think I'm going to faint!" – a reference to The Years' graphic backstreet abortion scene, which infamously made theatregoers pass out.

"It was so intense," says Garai. "It didn't totally blindside me because the piece was originally staged at the National Theatre in Holland and the director warned me that people had fainted. I was like: 'That won't happen here. We're British, we're not fainters! We do Coriolanus and Sarah Kane plays. I've been in shows where people's hands have been chopped off.' But the first time I said the word 'foetus', it was bang, bang, bang. People were just hitting the deck. It happened almost every night. Out of 53 performances, I'd say it happened 51 times. Extraordinary. I doubt I'll experience anything like that again as an actor."

With Adultery, she's about to shock a whole new audience. "I'm hoping I'll get lots more cheating wife roles," she says. "I was in my nun era, playing a lot of buttoned-up characters. A sort of a professional cross lady. Now I'm hoping to be a sexy untrustworthy wife. Entering my midlife sexpot era. That would be great."

Adultery starts this October on ITV1 and ITVX.