Matthew Rhys was filming the second series of the hit show The Americans, about an apparently American suburban couple in the 1980s who are in fact Soviet agents in an arranged marriage, when truth started blending into fiction. Not that the Welsh actor was recruited by the KGB, but that he began falling for Keri Russell, the American actress playing his wife.

“It terrifies the producers when that happens,” says Rhys, 50. “It’s understandable. These things often end quickly and then the set isn’t a pleasant place to be.” So he and Russell were at pains to keep their relationship secret. Then one night at about 3 a.m., when he was staying at her New York apartment, they heard burglars enter.

Rhys and Keri Russell originally kept their relationship a secret on the set of The Americans.

“It was very early in the relationship,” he says. “I remember thinking stupidly, ‘My next course of action will define how Keri sees me for the rest of my life.’ So if I say, ‘Let’s lock ourselves in the bathroom and call the police,’ she’ll think I’m a coward. The bedroom had a fireplace so I grabbed a poker and I made my way out, as dumb as you like. What was I thinking?”

Mercifully the burglars ran away when they heard him but they took several items they’d shoved into Rhys’s backpack. The police were called and quickly caught the felons. They then demanded payback in the form of a photo-op on the set of The Americans. “Keri was like, ‘No, no!’ but they came to give her stuff back in front of the cameras. One of the PAs was like, ‘That’s not Keri’s backpack, it’s Matthew’s! And isn’t that his watch?’ I said, ‘No, definitely not,’ but everyone started piecing it together.”

So the couple were busted. “And so many people on set were like, ‘I always knew from the first season,’ and you go, ‘Well, you didn’t, because there was nothing going on then.’ After that every day we’d see the look of concern on the producers’ faces: ‘Please, don’t split up and hate each other.’”

Happily this didn’t happen. By the time season four was filmed Russell was pregnant, her bump concealed by carefully positioned salad bowls, coats and CGI. Eleven years later, they’re still a couple (“we literally haven’t got round to marriage yet”). Rhys is talking over Zoom from their book-lined home — tomes include a biography of Richard Burton and Hands Off Wales by Wyn Thomas — in Brooklyn, New York, where they live with Russell’s two children, aged 17 and 13, from a previous relationship, and their eight-year-old son.

Yet not every day on set was hearts and flowers. “There’d be days when we were fighting and I’d be being as petulant and petty as I can be and we had to play a romantic moment.” And vice versa? “Well, yes. But not so often.”

Even before the reveal, one director had sussed them out. “It was an intimate scene and he was like, ‘That’s not the first time you guys have been naked together!’ It was like, ‘Oh my Christ! Shut up!’ You think you’re giving the performance of your life, not giving anything away, and clearly you’re as transparent as a pane of glass.”

In fact, before and after The Americans (for which Rhys won a best actor Emmy) he has been turning in top-notch performances. There was the 2008 film The Edge of Love, in which he played Dylan Thomas, a recent cameo as a narcotics officer in the unlikely Netflix smash Cocaine Bear, the role of Perry Mason in the recent HBO reboot and that of the journalist Lloyd Vogel in the Oscar-nominated A Beautiful Day in the Neighborhood, opposite Tom Hanks.

Rhys played the titular role in HBO’s legal drama Perry Mason.

Now he’s occupying the BBC’s cozy Sunday night drama slot by appearing in the Agatha Christie adaptation Towards Zero. For once there’s no Poirot or Miss Marple: he’s playing a far more nuanced detective, the shell-shocked depressive Inspector Leach. “Someone told me recently I always play depressed and put-upon people. I think it’s just the structure of my eyes. I have a Celtic lid, slightly hooded, that gives you the Eeyore look for free,” he says cheerily.

Towards Zero has a hyper-starry cast, including The Wire’s Clarke Peters and Anjelica Huston as the hostess of the country house where suspects gather. “She’s true Hollywood royalty,” Rhys says. “When I’m in the room with someone of that kind of caliber, impostor syndrome still hurricanes through my body. You’re like, Anjelica Huston will be the one to say, ‘Why are you here?’”

Affable, entertaining but clearly with an actor’s sensitive nature, Rhys grew up in Cardiff, the son of two teachers. Until he went to primary school he spoke Welsh exclusively (now he speaks it with his son, who is rebelling, saying he prefers “Mama’s language”). Having starred as Elvis in a play at his comprehensive, he was inspired to try auditioning for Rada, where a friend from the year above — Ioan Gruffudd (Hornblower) — had just won a place.

Rhys as Inspector Leach in the BBC’s Towards Zero.

After he graduated the work initially poured in, including the Dustin Hoffman role in the West End version of The Graduate, opposite Kathleen Turner as Mrs Robinson, who famously disrobed on stage. A tabloid newspaper sent a photographer along one night to record this moment. “Kathleen dropped her towel and a flash went off, and I saw the woman photographer in the royal box. I was 25, old enough to go, ‘Terribly sorry, ladies and gentlemen, we’re stopping the show while we retrieve the camera.’ But I looked to Kathleen, who is no shrinking violet and definitely the alpha in that situation. I thought if she wanted to stop the show she absolutely would, but she’s old-school and gave me this look of ‘no, we keep going’. But the next day it was all over the papers and I still regret not stepping up.” What was Turner’s reaction to the photos? “Very sad and disappointed.”

Soon after that he hit a dry patch, to the extent that he applied to join the army, but he got a rejection letter. “I kept that for a long time. I should have framed it.”

Aged 30, he moved to Hollywood and landed the role in The Americans. This gave him a — now extremely timely insight — into how Soviet intelligence had long done everything it could to destabilize the US. “It was dizzying to me that the Russians were so blatant and outlandish in their interference,” he says. ”The Americans’ head writer was a former CIA officer. I’d read his early drafts and say to him, ‘It’s just so far-fetched, I don’t know if people will believe it.’ And he’d go, ‘Well, that’s what they did.’

“The one that really got me was how in the 1984 Olympics in Los Angeles they were writing anonymous letters to the black members of the US Olympic team as if it was from white team members, saying they had no place on the team. It’s what they do so well — turning people in on themselves. It was so widespread and specific and dark and evil. I was, like, it’s not going to change any time soon. And now we’re watching it in real time and, sure enough, nothing has changed.” He rolls his eyes in alarm.

His expression shifts through several more gears of shock and dismay when I ask him how he’s finding life in Trump’s America. “That’s my face when I read the news. Every time you think things can’t peak any more, you go, ‘What? Really?’ It’s like watching a clown show but they’re juggling with chainsaws.” Is there palpable tension on the streets? “Yes, I said the same thing during his last administration. Everyone got edgier and angrier and chippier, and you feel it.”

He loves liberal Brooklyn — “it’s like living on a film set” — but does he want his son to grow up in the US? He frowns. “I never quite get to that point. But, yeah, I wonder about bringing children up in this country. When it’s these extremities, you go, what am I doing? Oh God, if you print that I’m going to take some heat. Social media will go, ‘Well, f*** off home then.’”

His patriotism runs deep. He’s used to patiently explaining to Americans that the Welsh language isn’t just accented English (“sometimes I can’t be bothered and just let them go with it”), but so far he’s flailing in his mission to make films with his production company about Welsh stories. “Scotland and Ireland get all the glory!” he exclaims. He’s been trying for 15 years to make the story of the medieval leader Owain Glyndwr. “People say, ‘But this is just the Welsh Braveheart.’ I say, ‘I know! And look how well Braveheart did. And we have an entirely new generation of people ready for it.’”

His acting career’s going much better — he’s just finished The Beast in Me, a Netflix series with Claire Danes, and is now on to an Apple TV+ project called Widow’s Bay, where he’s the lead. Surely that impostor syndrome is diminishing a tad? “Not at all. I remember when I worked with Anthony Hopkins for the first time and he said, ‘I’m always waiting for someone to say, “Not that Tony Hopkins, the other one.”’ It was one of those depressing moments when I thought, oh no, it never leaves you.”

Towards Zero premieres on BritBox on April 16

Julia Llewellyn Smith is a journalist at The Times of London