Kwame Kwei-Armah barely has time to be interviewed. We’re at the Ritzy Cinema in Brixton, where he’s about to chair a discussion to mark the anniversary of the tele-vision miniseries Roots. Tomorrow he’s in Chicago to watch a local take on his 2003 Hackney gun-crime smash Elmina’s Kitchen. Then he returns to see his newest play, Statement of Regret – inspired by Tony Blair’s speech about Britain’s role in the slave trade – open at the National Theatre. At such a time you or I might feel a bit wired. Kwei-Armah is no different, offering up steam-roller positivity alongside a torrent of studious perspectives on black culture, amid waves and high fives with almost everyone in the Ritzy café.

Mind you, he’s no stranger to multitasking. When he emerged as a major playwright four years ago, he was better known as an actor (Finlay Newton in Casualty on BBC One) and as a wannabe singer (he was runner-up on Celebrity Fame Academy). But the acting career is harder to sustain these days. “I’m told now that people don’t cast me because why would a director want to work with someone who directs and writes as well?” Kwei-Armah, now 40, has come to accept that play-writing is activity number one. Which is fine, because “I love being a writer”.

But he’s not just a writer. Not for Kwei-Armah art for art’s sake. “I am using art,” he says, categorically, “to be a catalyst for debate around themes that are pertinent to our communities and to our nation.” That’s an old-fashioned way of looking at the playwright’s craft, Kwei-Armah agrees. “But my role models are [the late black playwright] August Wilson in America and David Hare here. I am a political being,” he says, “and to deny that would be to deny access to my muse – whatever that is.”

Kwei-Armah’s chat – assertive, fastidious, precisely articulated – can sound as if it is being delivered from a soapbox. Fortunately, he is also uncynical and refreshingly eager to believe that the world is becoming a better place. How many black activist-artists would describe Britain today as “so much clearer, brighter and more honest than it has ever been when it comes to notions of race”? This, he insists, is the result of this year’s bicentenary commemoration of the abolition of the slave trade. “To have discussed the issues surrounding that, and to be encouraged by the state to do so,” he says, “has moved us closer to a healing than anything before.”

Which brings us to Kwei-Armah’s new drama for the National. The last time we met, as Elmina’s Kitchen became the first black British play to open in the West End, he told me that the third play in his black Britain trilogy (the second was Fix-Up in 2005) would be set in a church. In fact, it takes place in a black policy think-tank. The National Theatre supremo Nicholas Hytner turned down the church manuscript, Kwei-Armah says, “because it was too culturally specific. And that’s a wonderful thing, to have someone who can say no.”

Wonderful? To be rejected? Sometimes Kwei-Armah’s positivity can seem practically robotic. But then, Hytner is his mentor. “I am eternally grateful to Nick Hytner, who has allowed me to have a voice.” But shouldn’t Hytner be grateful to you for writing him such good plays? “He would be wrong to be,” Kwei-Armah insists. “It’s me that is grateful.”

He’s now expressing that gratitude with a new play about “post-traumatic slave syndrome”, a term coined by the American academic Dr Joy Leary. “I heard an interesting quote,” the playwright says, “ ‘We were an enslaved people, and we are still haunted by memories of that enslavement.’ Is that true? Are we still mentally enslaved?”

When Tony Blair made his “statement of regret” about Britain’s role in the slave trade, Kwei-Armah thought: “I’ve got to write something around that.” What fascinated him was that the Government’s legal advisers vetoed an apology lest Britain be rendered liable for damages. (The African-American community is currently suing the United States for $77 trillion in reparations). “If the legal department of Government is worried,” Kwei-Armah says, “then there must be an element of truth in the claim. So let us explore that. What happens when one seeks to repair? We often think it’s just money: every black person will be given five grand to buy a new BMW. I’m not thinking of that. I’m thinking of reparation as healing.”

In Statement of Regret these issues come to life as a debate between a father and his sons, and between older and younger members of the Institute of Black Policy Research, about which issues a black NGO should be airing. Reparations for slavery? Or domestic violence and low educational standards in the black community? The old-school campaigners want a united front against white oppression. But, as the new generation argues, “self-flagellating liberalism is dead . . . the money is in self-criticism”.

Is this how Kwei-Armah sees the state of racial politics? “Absolutely.” As a reaction against political correctness, he says, and specifically after the 7/7 London bombings, “society, and that includes black people, started to think: ‘We’re bored of whingeing blacks. It’s time they looked at their own problems. The time is past for blaming the white man.’ ” He pauses. “There are elements of truth in that, but it is certainly not the whole truth.”

Another major strand in the play dramatises community rivalries within black British culture, as the protagonist Kwaku Mackenzie argues that reparations should be targeted exclusively towards those of Caribbean descent. “I was worried about exposing those antipathies,” says Kwei-Armah, whose background is African-Caribbean. “But a lot of things have been swept under the carpet. My generation moved from a position of abusing African children, because we had received notions of their inferiority via Tarzan movies and the mechanisms of empire, to deciding, by the 1980s, ‘we’re all African’.” Kwei-Armah was born Ian Roberts and ditched his “slave name” in his late teens. “My personal view,” he says, “is that we are all Africans.”

But differences between (and within) the two communities remain. “Right now the children who are failing are from the African-Caribbean community, and that needs specific action. To just merge it with ‘the black community’ is problematic.” KweiArmah also believes that his own cultural group is in decline. “Within five years, when we discuss black Britain, it will no longer be the Windrush generation, it will no longer be pork-pie hats or young Rastafarians. It will be new African migrant stories. Because demographically, the African-Caribbean is shrinking and the West African community is growing. And that will create tensions.”

And, as like as not, Kwei-Armah will be dramatising them. But even now, with his plays produced around the world, he feels “an element of fear that what I have to say I need to say now, before I am no longer in vogue. Because, historically, only one or two black people are allowed in at a time, and then you’re quickly ejected. But I do feel that I’m standing on slightly firmer ground now.”

So can we expect more “debates around themes that are pertinent to our nation”? “I’m not speaking on behalf of the nation,” he says. “I’m speaking on behalf of myself. I’m discussing in my plays the things that I discuss in my front room with my children, that I have discussed over the years with my parents. What I write is the theatre of my front room.”

Statement of Regret previews at the National Theatre (020-7452 3000), from November 7

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