Kwame Kwei-Armah’s imposing face has just been splashed all over the news. Last week he was appointed artistic director of Young Vic in London, one of Britain’s most prestigious theatres. It’s a great job, make no mistake. But there was something more to it than that. He is the first African-Caribbean director to run a major British theatre.

Earlier this year he handed in his notice in Baltimore, where he is artistic director of the Center Stage theatre. In the US he is out on his own, too. Last year he described the situation as “almost sinful”. Today, if anything, he feels even more strongly about it. “In America, I am the only black male artistic director of a major theatre. And we’re talking about 100 top regional theatres. And in Britain, I will be the only African-Caribbean director of a major. And in Europe, I don’t know of any, which tells me that in the western world there is only one diasporic African artistic director of a major theatre, and that is what I mean by sinful.”

He stops, to make it clear that he’s not bragging. “It can sound like a boast, but that is systematic inequality. I cannot believe there is only one person that can hold the reins of a major cultural institution. It doesn’t make sense. Therefore it has to be systemic.”

Rarely has an appointment been greeted with such approval. Kwei-Armah’s accomplished CV is highly unusual for an artistic director. Whereas a number have been successful actors, it is almost unprecedented for artistic directors to also have a formidable record as a playwright. Kwei-Armah has proved himself in all three fields – as an actor, he played paramedic Finlay Newton in Casualty for five seasons; his plays Elmina’s Kitchen, Fix Up and Statement of Regret were all staged at the National Theatre; and in 2005, he became only the second black British playwright to have his work put on in the West End of London when Elmina’s Kitchen transferred. In 2003, he even sang on Celebrity Fame Academy.

Facebook Twitter Pinterest Kwei-Armah in Elmina’s Kitchen in 2005. Photograph: Tristram Kenton/The Guardian

Kwei-Armah, 50, was born Ian Roberts to working-class parents from Grenada who settled in Southall, west London. In 1979, aged 12, he witnessed the Southall riots – police chasing black and Asian boys along the street with batons and shields followed by skinheads. One day, not long after, the police kicked down the family’s front door, sending his younger brother flying. They ran upstairs to his father’s bedroom, breaking open his wardrobe and ransacking the place. His father had never been in trouble – and he was not charged with anything. That was when Kwei-Armah’s mother said to young Ian: “I need you to be a lawyer.” She felt the family could only be protected if they had a foot in the establishment. But he wasn’t having any of it – he was set on a stage career, preferably as an R&B singer. His father worked at the Quaker Oats factory and his mother held down three jobs (nurse, nanny and hairdresser) to put him through stage school.

As a child, he did not just face racism from white people. Lighter-skinned black people told him he was too dark, his nostrils too flared, his lips too thick. Teachers told him the structure of his mouth stopped him from speaking properly. A female cousin told him that if he pinched his nose a few times a day, he could streamline it – after a few weeks he gave up.

Unsurprisingly, he was soon politicised – not least by the writings of Malcolm X and the TV series Roots, about African American Alex Haley tracing his lineage back to Kunta Kinte in Gambia. At the age of 19, he started to research his own family tree, through the slave trade back to his ancestral roots in Ghana. At 21, having graduated from the Open University with a degree in African civilisation, he announced that he was no longer Ian Roberts; he was changing his name to Kwame Kwei-Armah. Kwame means “born on a Saturday” (he was actually born on a Thursday) and Kwei-Armah means “to find the way”.

We meet at the Donmar Warehouse in London, where he is directing rehearsals of Ibsen’s The Lady from the Sea. He is as stylishly dressed as ever – muslin shirt, bomber jacket, tracky bottoms, huge loafers (size 12), cerebral specs, all black, set off by yellow Buddhist beads.

Facebook Twitter Pinterest Kwei-Armah and Finbar Lynch in rehearsals for The Lady from the Sea at the Donmar Warehouse. Photograph: Manuel Harlan

I last interviewed Kwei-Armah 14 years ago, when he had just premiered Elmina’s Kitchen (a play set in a West Indian restaurant in Hackney that tackled his great fear – black boys who felt they had to conform to a gangster stereotype). The transition to playwright was a huge moment for him. Kwei-Armah was in his mid-30s, ebullient, great fun, puppyish in his enthusiasm. He’s still got that great roar of a laugh, but he seems different – quieter, stronger, less try-hard.

The job in Baltimore was a fantastic opportunity not just to run a theatre, but to build one virtually from scratch. And there was another draw. Kwei-Armah went over in 2011 with his second wife, Michelle, and their son Iyare, then aged five (he has three children from a previous marriage): “The idea that Iyare would grow up under Obama was so intoxiating and beautiful.” But he ended up experiencing something very different – a wrecked economy, widespread poverty, people divided increasingly along racial lines, the fallout from Obama’s presidency, the rise of populism. “What I’ve seen over the years is the rise of rage; the rise of a true understanding that disparity and inequality is deeply baked into our system, and that’s for white folk, too.”

Sometimes he experienced the rage first hand. He tells me a story of a train journey he took from New York to Baltimore. “I had my laptop open and was writing. A white male sat opposite me, probably in his late 50s. He was drinking and leant over and asked: ‘Are you one of those scary black men ’cause I’m afraid of black men and spiders.’ He then spilled bile for about 45 minutes. I said absolutely nothing, just going ‘OK’, trying to calm him down. In the end, he got up and put two fingers into the shape of a gun and went to my brain and said: ‘That’s what we should do with you,’ and he just went ‘BAAAAAAANG!’”

I jump, shocked.

“That’s the level of rage that was bubbling coming up to the election,” Kwei-Armah says. “So Trump’s victory was not a surprise for me.”

Meanwhile, the Black Lives Matter movement was taking off after 17-year-old Trayvon Martin was shot in Florida and his killer, George Zimmerman, was acquitted. Kwei-Armah says it is only recently he has begun to realise what an impact the movement has had on him – personally, politically, professionally. “The day Zimmerman was released, I walked around Baltimore and for the first time in my life I saw existential angst and fear in the eyes of the black community. Mothers and fathers going: ‘I don’t know how to protect my children. I used to say, just put your hands up, don’t answer back, these are all tools that will save your life, and now I don’t know.’”

At the same time, Kwei-Armah was being challenged at the theatre. “People were saying: ‘Kwame’s doing too many black plays.’ I was actually doing the same number that had been done by my predecessor, though she was white, so possibly they perceived that as an act of philanthropy and mine as an active agenda.”

Facebook Twitter Pinterest Kwei-Armah as Finlay Newton in Casualty. Photograph: John Rogers/BBC

Rather than give in to the pressure, he went the other way, hiring 10 writers to go into the poorest areas of the city, talk to people and write plays about their experiences. The more killings there were, the more activist his theatre became. He commissioned 50 American playwrights to write plays about how the country was changing and shot them as videos. “We shot on the spot where many of the black men were killed – Michael Brown, Trayvon, Eric Garner. We’d shoot what I called Rapid Response Theatre, five-minute plays. We did it while a funeral was happening in Charleston after nine black people were killed in the church. We got shut down by the police, we got run off estates.”

You seem so different, I tell Kwei-Armah, more grownup. He smiles, and says he had a lot of growing up to do in the US – and quickly. He had never run a theatre, or managed budgets and staff. “At times I felt out of my depth.” He oversaw a $32m (£24m) transformation that turned an unwelcoming space into a sophisticated complex with two additional theatres. The funny thing is, he says, he took his board over to the Young Vic in London to show what he wanted his theatre to look and feel like: warm, bustling, alive, social.

He was also determined to change the demographic of the audience. Despite the fact that Baltimore is 65% African American, only 11% of the audience were. “The theatre itself was almost sending out signals saying: ‘It’s safe for you to come from the counties into the theatre.’ Our box office had bullet-proof glass, and I was like: ‘This is closed, not open, and we need to send out the signs that we are open.’” Now, 22% of the audience are African American.

How did he change things? He smiles. “Event theatre. To get new people in, I needed to put on plays that made them go: ‘Oh, I get brownie points tomorrow at work having seen it.’ It was difficult to get star names to come to Baltimore, so I created plays about stars. I found a play, One Night in Miami, about Muhammad Ali and Sam Cooke. All of a sudden, people went: ‘Oh, I want to see that play about Muhammad Ali.’”

It was April 2015 and they were deep into rehearsing a musical he had written about Bob Marley when Baltimore rioted after 25-year-old African American Freddie Gray died after sustaining injuries to his neck and spine in a police vehicle. “There was so much pain on the streets in Baltimore. I said I’d like to take the cast to the point of the disturbances, and sing all the songs from the show. We took a vote and all the cast said: ‘Absolutely.’ There was just a mic and some speakers and within 10 minutes about 300 people had gathered. People were dancing in the street, and drivers were beeping their cars. It was like Fame! Then the National Guard, who were on patrol, started walking towards us and I was like: ‘They’re going to shut us down.’ They came up and went: ‘Can you do Three Little Birds?’” Kwei-Armah rocks with laughter. “That will be with me all the days of my life.”

I am left open-mouthed by Kwei-Armah’s stories – and his achievements. I think back to the eager-to-please young man I met on the South Bank 14 years ago. You seemed hyper then, I say; more actorly. “Yeah, I’d buy that,” he says. “I think I’ve been trying to answer a lot in my life. People go: as a black male, you can’t do this. And I think I’ve tried to go: yes, we can. That’s the box you want to put me in? Well, I’m not going to allow you to put me in that box.” Can he give an example? “Yes, my accent. I taught myself to sound like this. Really, when I’m at home I sound far more estuary. I do a lot of: ‘Yeah blud! What ya talkin ’bat?’”

In other words, he says, he might have defied stereotypes by speaking the Queen’s English, but he was still allowing others to set the terms of his rebellion. “I finally went: ‘Stop seeking approval, no matter how subconscious it is. Stop! Just be!’ I think maybe that is a difference in me in the last 14 years.”

So he started doing things just for himself – street theatre, ensuring that at least 50% of the plays he put on were written by women, insisting that the classics were directed by people of colour so they could never be told they lacked sufficient breadth when applying for top jobs.

After the theatre’s refurbishment was complete, Kwei-Armah handed in his notice. Why? “I got a feeling in my stomach that I’d done what I came there to do. I thought if I stayed it would just be to play with the toys and for the wage.” His family thought he was bonkers.

He won’t be leaving until next year, when he will replace the hugely respected David Lan, who has been at the Young Vic for 18 years. “When it was announced David was leaving, everybody was asking me if I was going to go for it. Then I met with David, and I threw my hat into the ring.” It is only three weeks since he was interviewed by a panel of the great and the good, including Stephen Daldry. How did he convince them he was the one? He grins. “I said the Young Vic is funky, and I love me some funk. Then I was fortunate enough to be offered it.”

The Young Vic is not known for new writing. Will he introduce more? “Of course I’m going to do new plays. But the Royal Court does that too, so it’s finding the right new plays.”

Facebook Twitter Pinterest Kwame with the team from Fame Academy. Photograph: Tony Kyriacou/Rex/Shutterstock

Kwei-Armah says that for all he’s changed, he’s still in touch with the 19-year-old Ian Roberts who decided it was time to find a new identity. “My 19-year-old self is the person I judge myself by. The 19-year-old Ian saw the world in a really clear fashion. I can sometimes call it pragmatism; he would have called it compromise. He saw truth without the complication of responsibility.”

What would 19-year-old Ian say to him? I think there would be some disappointment. I think I’d have to explain some of the choices I’ve made. He would look at the demographic that go to theatre, and say: ‘Who are you talking to?’” What would he answer? “I’d say I’ve tried to make theatre more accessible because I believe in it as an art form. I love it, and I can bring more people to this brilliant art form.”

His beloved mother died 12 years ago. Does he think she would be happy about the new job or still want him to be a lawyer? He looks on the verge of tears. “I think she would love the glass ceilingness of it. I think she would hug me and be very, very proud.”

The Lady from the Sea is at the Donmar Warehouse, London, from 12 October, donmarwarehouse.com.