Michael Sheen is at home in south Wales, looking out on his garden. The sun catches the side of his face, lighting up his scraggly hair and beard. “We’re very lucky to have a garden to go out in. I know not everybody does,” he says. In the current climate of famous people churning out endless videos of their isolation struggles from the side of a pool in a mansion, it’s a telling sentiment.

A few years ago, after a successful stage and screen career, the actor, 51, “refocused” his life away from entertainment towards community work and activism, and moved back to Wales from Los Angeles. He had been living there for much of the past two decades, to be near his eldest daughter, Lily (her mother is the actor Kate Beckinsale, and they remain close). “And then when my daughter was 18 and went off to a life of her own, I realised: ‘Oh, I can go home again now.’”

He has a new daughter, six-month-old Lyra, with the Swedish actor Anna Lundberg, and the baby burbles away in the background as we speak. Having a young child has given him a sense of routine during the current crisis. He went on Newsnight recently, to talk about clapping for the NHS, which he called “that wonder of the world”. The presenter, Emma Barnett, asked him for an isolation coping tip. “And I said well … the baby has a routine, and I’ve found that that’s helping us. And then I noticed that somebody said that was an example of my condescending class-blind privilege,” he says, smiling, and shakes his head.

Sheen grew up in Port Talbot and there is a long history of showbiz in the family. His great great grandmother was an elephant- and lion-tamer, and his father spent some time as a Jack Nicholson impersonator. How does he define himself, in terms of class? “God, I’m not really sure,” he says, “I came from a working-class town, my family was a working-class family, for generations. My dad got a job in middle management at a certain point, and I suppose that took us up a step. My mum worked as a secretary, my grandmother was a cleaner at the local police station. But then I went off and became a successful actor. Middle class, I guess?”

As Brian Clough in The Damned United. Photograph: Sony Pics/Everett/Rex

Sheen feels a strong connection to the community he grew up in. “More and more as I’ve got older, it’s been that which has guided the choices I’ve made, about what it is I want to do with the privilege and the resources that I do have,” he says.

Moving back to Wales changed his life considerably. He set up a production company, Red Seam, to develop specifically Welsh stories. “We have these incredibly big productions coming over here and using our locations and infrastructure and talent,” he says, “but those stories are not about Wales.” Sheen has so far managed to avoid the criticism faced by many famous people when they “get political”, probably because he isn’t paying lip service to it. He really is there, doing the work.

Acting was supposed to be on the back burner, yet Sheen has continued to appear on screen. Over the past couple of years, he has been in Good Omens, The Good Fight and the US drama Prodigal Son. “I’ve actually ended up spending the last six months in New York working, which is not what I intended,” he says. “But when I gave all my money away, I suddenly had to go and earn money again.”

He says he gave all of his money away to bring the Homeless World Cup to Cardiff last summer. With eight weeks to go until the big charity event, “someone completely fucked us over”, says Sheen, leaving him with two weeks to come up with enough money to keep it afloat (event organisers have said it costs £2m a year to put on). “Five hundred of the most vulnerable people from all over the world [were] on their way to Cardiff, for a tournament that was potentially transformative and life-changing. And so,” he says, as if it were the easiest decision in the world, “I gave all my money to it.” He will be paying it off for years, he adds, cheerfully, which explains why he’s working in the US again, on Prodigal Son. But, he says, tactfully: “It’s not like I’m forcing myself to do it. It’s a great job.”

Soon, Sheen will return to British television, playing Chris Tarrant in Quiz, a three-part adaptation of the James Graham play that tells the story of the infamous “coughing major” cheating scandal on Who Wants To Be a Millionaire. Its director, Stephen Frears, got in touch to see if Sheen would be interested in playing Tarrant. “Like most people, I felt like I’d seen those episodes. Then I subsequently discovered they never got transmitted, so nobody had seen those episodes,” he says. I’m shocked. “ITV rushed out a documentary about it, literally the next week or something like that. So people think they’ve seen it, but actually what they saw was the documentary, which was certainly true in my case.”

Sheen is well-known for playing real people: Brian Clough in The Damned United, David Frost in Frost/Nixon, Kenneth Williams in Fantabulosa! and Tony Blair, three times, in The Deal, The Queen and The Special Relationship. Is there a sense that whoever is casting Sheen has seen something of that real person in him?

“I suppose I have to assume that,” he says. “It’s not just, oh, Michael does real people, let’s get him in to play whoever. When I look at all the real people I have played, the majority of them tend to be quite flashy. If you wanted to be ungenerous, you could say there’s a bit of surface razzle-dazzle covering over slightly more questionable qualities. Not that I’m saying that’s Tarrant,” he adds. “But that kind of frontman, the person who has lots of apparent confidence and ease.”

He has always chosen not to meet the people he will play. “Once you meet someone,’ he says, “inevitably you want to take responsibility for them. And no matter how it goes, if you really get on with each other and you really like a person, inevitably you will shy away from certain things.” He did end up meeting Tarrant, a couple of days after he had finished filming Quiz. “Just coincidentally, I bumped into him at the Pride of Britain awards. I was having a photograph taken, and I heard a voice going” – he slips into an impeccable Tarrant – “‘You don’t look anything like me.’ And there was Chris Tarrant.”

Just before he started work on The Special Relationship, which came out in 2010, he met Blair for the first time. By that point, he had already played him twice, and felt comfortable enough to meet him. “He was very wary of me,” Sheen recalls. “It was interesting because he’s clearly someone who is very socially charming and engaging, and clearly wants the social interaction to go well.” He knew this anyway, he says, from all the research and work he had done. “But I could see that actively happening, at the same time as this other part of him was going: ‘Hang on, this guy might be copying me.’ There was an odd dynamic there. Also, it was very peculiar circumstances.”

This turns out to be an understatement. “It was at the Murdoch residence in Los Angeles,” he begins. He had been introduced to Wendi Murdoch, as she was at the time, at a charity event in New York. “And someone had said to her, that’s the guy who plays Blair. And she got very excited about this. She said: ‘Oh, I’m having a dinner for Tony soon, you must come.’” His curiosity about meeting Blair got the better of him. “It took a little while for it to dawn on me: oh, but it’s going to be at Rupert Murdoch’s house,” he says.

Sheen as Tony Blair in The Queen. Photograph: c Miramax/Everett/Rex Features

Before the party, Wendi had emailed. “She would get in touch with me and say, maybe you could make your hair look like him? Maybe you could dress like him, and we could hide you, and bring you out, and surprise him? I remember writing back to her in an email and going: ‘I don’t want to put anyone in an uncomfortable position, so I think we should just leave it.’ I thought, she’s going to have me jumping out of a cake or something.”

She told him not to worry, and to come along anyway. He drove to the party, in the Hollywood Hills. “Suddenly I found myself face-to-face with Tony Blair,” he says. “And he found himself face-to-face with me, with a group of people suddenly around us, and Wendi Murdoch saying: ‘Tony? It’s you!’”

Another guest asked Blair if he thought Sheen’s portrayals had been accurate. Blair replied that he had not watched any of the films. “When people dispersed and it was just me and him, he started talking in fairly minute detail about individual scenes,” says Sheen. Before they sat down to eat, he had an encounter with Rupert Murdoch himself. “There was a very peculiar moment with Murdoch. I remember standing looking out at the view, and then I realised that Murdoch was standing next to me. It was quite a hot day. I just remember seeing a little bead of black dye, running down his face.” He drags a finger from his forehead down the side of his cheek. “I thought, oh, Ozymandias.”

Sheen is fascinated by Blair’s legacy now, by how his personal popularity has been shredded and how deep divisions about that era continue to rage within the Labour party. But the relationship he has with the real people he has played is a strange one. “Obviously, Blair is someone I played the most,” says Sheen. “It feels like a very long time ago now so it’s not quite the same, but I still can’t quite trust what I feel. Because there’s still a little bit of me that when I see him or read about him that I’m sort of seeing myself. That’s a weird thing to have.”

When it comes to the current prime minister, he is less ambivalent. “I don’t know [Johnson], I’ve never met him,” says Sheen. “But my fear is that he’s someone that it’s all a game to. It’s very hard to avoid the feeling that he’s still playing games in a common room at his school. Aside from being totally opposite to his politics anyway, just as a personality, it’s all a game, it’s all about winning the debate, the empty debate. There’s no real heart there, there’s no real commitment there, to anything.”

Sheen finds the existence of the two versions of Johnson’s column on Brexit, one arguing for remain, and one arguing for leave, particularly abhorrent. “One of the most consequential and divisive things in our cultural life, and the man who was at the forefront of it could have gone either way, really.” He says this as if still astonished by it. “It’s very hard to trust someone who can go so easily in different ways.”

Sheen has done so much political work, from campaigning to end high-cost credit agreements to trying to help find a solution to the crisis in local journalism, that he is often asked if he harbours political ambitions.

“I think my condescending class-blind privilege is getting in the way, to be honest,” he says, smiling. Since he moved back to Wales and focused on community work, he has realised it is no longer enough to simply tell people what they are doing wrong. “I’m part of now trying to come up with a better way, rather than just criticising the way other people are doing things,” he says. “I have to work with people that I really disagree with, or I have to try and find a way to compromise or find a way forward with people who you really don’t agree with.”

As the situation stands, Sheen does not have to toe any party line. “I could walk away from it all, whenever I want, and I’d be fine, and there’s a strength in that,” he says. “I’m not sure what I’d gain by giving that up, right now.” So he has no interest in running for office? “I used to say, there’s only one community that I feel that I could in any way justify representing, and that’s the community that I grew up in, and that position is already taken.” It’s taken by Stephen Kinnock, MP for Aberavon. “But of course, he might be arrested for visiting his father, so that role might become vacant very soon,” Sheen says. He is joking, though part of me hopes he might one day take the idea of Michael Sheen MP seriously, after all.

Part one of Quiz is on at 9pm on 13 April on ITV