It’s the new test of whether or not a play has really got you: can you read the whole thing on your phone?” says David Harewood, gesturing towards a small screen with an eye-strainingly tiny typeface. “I did and I thought, ‘That’s bloody good, I want to do it.’”

His instincts weren’t wrong. Reading the piece in question, The Mountaintop, in conventional form, reveals a sparkling new two-hander set in that fateful Memphis motel on 3 April, 1968, the night before Martin Luther King Jr was assassinated.
The script, directed at Battersea’s Theatre 503 by James Dacre, is the work of award-winning young American playwright Katori Hall.

It crackles with humour as well as poignancy, as a weary King (Harewood) winds up reviewing his life, and the achievements and failures of the civil rights struggle, in the company of a beautiful young chambermaid (Lorraine Burroughs) who turns out to be not quite what she seems.

“It’s going to be interesting,” says the impressively eloquent yet self-contained Harewood. “I think that people are expecting to see this rather pompous, self-important character that King was sometimes reported to be. But he was actually a very playful man. The public face was the guy who was making all those great speeches but the private King was a man who was forever joking around, drinking, smoking and womanising.”

This appealingly human aspect of King dominates the play’s quickfire early exchanges, as he flirtatiously invites comely Camae to stay and share a cigarette with him. One of the themes that struck me most forcefully was the idea of the inevitability of King’s martyrdom.

“It’s unfortunate, isn’t it?” Harewood asks. “‘Greater the man who gets more done dead than alive’ is the line in the play, and there’s an argument that says it would have been impossible for King to achieve all this” — he sweeps his hand towards the hotel window and the bustling, cosmopolitan London street outside — “had he still been alive.”

He paved the way for Obama, though, didn’t he? “That’s the point the play is making — yes, we have come so far in some respects but our advancement doesn’t stop with the election of Obama. It makes me reflect on where we are here.

Diversity may have won Britain’s Got Talent but we’ve got the growing menace of the BNP, our young boys dropping out of the education system and the lack of growth of any substantial black middle class.”

Intriguingly, King is not the only epoch-defining political figure that Rada-trained Harewood, 43, has tackled this year. One of the foremost stage (Antony to Vanessa Redgrave’s Cleopatra in 1995, for instance) and screen (Blood Diamond with Leonardo DiCaprio) actors of his generation, he has recently finished filming the role of Nelson Mandela alongside Sophie Okonedo’s Winnie, in Mrs Mandela, a one-off BBC drama around which a gentle buzz is already building. Then there are his ongoing television roles as Friar Tuck in Robin Hood, as well as the recent Bafta-winning thriller Criminal Justice.

I’m fascinated, I tell him, by a comment that former Spooks star David Oyelowo made in an interview a couple of years ago, to the effect that at a certain stage, black British actors have to go to America to advance their careers.

“The market here is much smaller, and it’s run by a particularly small group of I would say probably white middle-class men and women,” Harewood says, though without any hint of bitterness.

“Most of my contemporaries have gone to America because there doesn’t seem to be that same hang-up about colour, and you can play characters with weight and authority, which here we still struggle to do.”

So will he be crossing the Atlantic any time soon? “I’m going to have to at some point, I suppose. I could probably get by here playing guest leads and second leads, but I must admit the older I get, the more frustrating it is. I would like to try and challenge myself a bit more.”

It’s hard to think of a greater immediate challenge than bringing off Hall’s fizzing dialogue in the tiny confines of Theatre 503. “I was hoping that the phone call from my agent would be the next big Hollywood film or a nice chunk of telly work, and then someone says: ‘Do you want to do a show in a theatre above a pub in Battersea?’ You kind of go...”

He smiles. “But I was really moved by the power of the script — and it’s taking me right back to why I wanted to act in the first place.”

The Mountaintop is at Theatre 503 until 4 July. Box office: 020 7978 7040, www.theatre503.com