n a London hotel room, Dominic West is weighing up how much he would accept to strip to his socks. In the new series War, West plays a social media billionaire who is supposed to be fairly decent, though there's one excruciating scene – goading someone to strip for money – that reveals he's definitely also a bit of a git. "That, I suppose, is the kick billionaires must get: that people would do anything for money," he says. He wonders what his price would be. His co-star Sienna Miller laughs and says he'd do it "for the lols", and West grins and says: "No, I'd want three figures. A hundred quid."

War is a juicy eight-part legal drama, where Miller and West are a divorcing couple – she a narcissistic film star, he said billionaire – so just about all their scenes together are suppurating with contempt, which is fun, but also a bit of a shame because they have such good chemistry. They first worked together 21 years ago in the West End production of Shakespeare's As You Like It. "So we had a history, which was great," says Miller. There have been many times she's gone into jobs where "on the first day you're married to someone and you don't know them. It's helpful to have some sort of rapport."

West was cast first – he had worked with the creator George Kay previously on the classy BBC drama The Hour, and Kay had written the role of Morgan Henderson, a tech entrepreneur, with him in mind. Miller plays Carla Duval, a Hollywood star who wants half of her philandering ex's wealth – with the help of her formidable legal team. Neither Carla nor Morgan have much to recommend them. Miller struggled, she says with a laugh, to "find the more human aspects of her, until I realised it was really fun not to. I decided to have fun leaning into the unappealing qualities of Carla, which was quite uncomfortable for somebody who errs on the side of people-pleasing. To not be invested in other people's reactions or responses. To be narcissistic, basically."

For West, it must have been just as tricky finding his way into playing a "benign billionaire". Do they exist? The BBC podcast Good Bad Billionaire came in useful, he says. Only a handful of the billionaires covered could be considered "good". "Basically they're the ones who give away all the money … It was intriguing to me, the idea of a benign billionaire." But Morgan obviously has a ruthless side – the hardball divorce negotiations, and that strip scene. "And you go, oh, we see why he's a billionaire. But other than that, I was doing what Sienna was avoiding, and I do all the time, which is desperately try to make people like me."

Was the high-profile divorce based on real-life cases? No, says Kay when we speak. Only one scene was inspired by real events – when the actor and director Olivia Wilde was served custody papers at a public event on behalf of Ted Lasso star Jason Sudeikis. "It was one of our most emotional days [on set]," says Kay, "because it's such a horrible thing to do."

The show was inspired by a conversation Kay overheard in a queue in an airport lounge. "This woman screamed 'Yes!' into her phone. I turned around, because I'm quite nosy, and said: 'Can I ask what has made you so happy?'" She told him her husband had finally signed the papers after a four-year divorce battle. The more Kay looked into high-stakes, high-end divorces, the more he realised it was filled with drama – the prenups, the affairs, the property – and ideal for the kind of glossy legal shows he'd grown up watching. "I'm a kid of the 90s," he says. He loved the big law shows such as Ally McBeal, and later The Good Wife, and The West Wing was inspiration as a workplace-based drama. "I loved the humour. I wanted to do something with the sort of zip and repartee of those shows." It's the reason the cast of War is so comedian-heavy, including Miles Jupp and Nick Mohammed as solicitors at rival firms. "People [who] are just super-sharp on the cues because if anyone slows down, it dies on its feet." (Extra fun fact: Mohammed and Celia Imrie, who plays a barrister, were also filming The Celebrity Traitors at the same time. "They were so tight-lipped!" says Kay.)

He had previously worked with writer Abi Morgan on her show The Hour; Morgan's series The Split also features glossy divorce lawyers, but Kay says his were "all American references". There's already a second series with the rival law firms taking on a defamation case. Expect more juice.

A public divorce brings wild scrutiny of the private lives of the people going through it, and when it's a celebrity couple – as Morgan and Carla discover – it's on a different scale altogether. Miller and West both have experience of this, though not in divorces. West had a brief period of what might politely be called "marital scrutiny" (in late 2020, photographers camped outside his house after photographs were published of him with his The Pursuit of Love co-star Lily James) but Miller had years of intense hounding during her relationship with the actor Jude Law. A victim of phone hacking by the News of the World, she won damages in 2011, gave evidence to the Leveson inquiry, and settled with News Group Newspapers in 2021 over alleged hacking.

"They [the paparazzi] were hounding you, weren't they?" says West, remembering scenes outside the London theatre where they worked in 2005. Yes, says Miller, "but it feels like another life and another world. It's now almost, from a kind of sociological perspective, interesting to look back on what the culture was like then."

What is curious, though, is why Miller seems so willing to put herself through it in her work: in War, as in Netflix's Anatomy of a Scandal, she's harassed by paps and dealing with an unfaithful husband. Having only got the later scripts after signing on, she didn't know what Carla would be dealing with. She laughs and says maybe directors instantly think of her for "that kind of storyline, which is something I'll now avoid". But does it stir up difficult memories, or is there a catharsis in playing it? "Maybe that's it. Maybe it is kind of reframing it for myself – to pretend at it, and to then remember how crazy that was as a way of living." Separately, Kay says his stars' personal experiences didn't influence the casting or writing. "One of the things we did quite quickly was we resisted any of that meta-referencing, because they are incredibly good actors, and these parts are different from their own experiences."

West has had plenty of accolades, but Miller has always been underrated; she has said that the emphasis on her personal life probably derailed her career. She puts in a wonderful performance in War, as she has in other roles such as the weighty 2018 film American Woman. "I feel less like I have to prove something, and I'm not sure whether that's because I don't have anything to prove, or I just don't care about proving myself any more," she says.

There are also a few better roles now for older women. "I remember speaking to actresses who were like: 'You're so lucky that you're turning 40 now, because we were obsolete when that happened.' But I still wish I'd played Juliet." She remembers speaking to a theatre heavyweight not so long ago and asking if he thought she could still play Juliet. She laughs as she remembers: "He said, 'I just think people will struggle to see you as a virgin.'" West adds with a laugh, "You just need an old Romeo."

Has this show put them off ever getting divorced? "Of course!" says West (married since 2010). "I think that's the big takeaway. I was talking to a guy who was rich and getting a divorce, and he backed up everything in the show. The interesting thing, and George anatomises it so well, is how two people who loved each other can descend into warfare. That's where the drama is: that knife edge between love and hate. You get it in any relationship, when you're arguing or whatever, but this is in a wildly expensive public arena. Like a battle in any commercial situation, with big lawyers, your marriage becomes that." A commodity, says Miller (she's engaged to the actor Oli Green), "to be bartered with, and the more acrimonious, the more money [for the lawyers]".

The stress and vitriol unleashed by this divorce, arguing over numbers so big they're almost meaningless, seems barely worth it. I'd have settled for a lot less to avoid it (I'd be a terrible divorce lawyer). "I imagine that kind of money to be incredibly corrosive," says Miller. "I have been in proximity to people who have a huge amount of money, and I just don't see them as happier. I mean, it's a revolting amount of money." West has given billionaires more thought recently than he'd probably like to. "If you've got several hundred billion, and you're not solving the climate crisis, then really something's deeply wrong."

War is on Sky Atlantic on Friday 2 October at 9pm.