The Wire hero Idris Elba's biggest challenge yet? To become Nelson Mandela in Long Walk to Freedom

Tyre fitter. Advertising sales cold caller. Wedding DJ. Nightshift worker at the Ford factory in Dagenham. These are some of the jobs Idris Elba took as he was trying to break into acting during his early twenties. Now, less than two decades on, his job description simply reads "global superstar".

It's a long way from East Ham to Hollywood, but Elba has made the journey apparently without breaking sweat. Before his 30th birthday in 2002, the actor from east London graduated from supporting parts in murder reconstructions on Crimewatch to the game-changing role of Baltimore drug kingpin "Stringer" Bell in The Wire, perhaps the most fêted TV series of the past 20 years. And now at the age of just 40, Elba is one of the most in- demand actors on the planet.

Following eye-catching roles in such films as American Gangster, Prometheus and Thor, the actor is starring in such eagerly awaited forthcoming movies as Guillermo del Toro's mega sci-fi blockbuster Pacific Rim and the biopic Mandela: Long Walk to Freedom.

Mandela is critically ill in hospital. Speaking about the role, Elba says, "To call the prospect of playing Nelson Mandela intimidating would be to put it lightly. But it's a massive honour to play this saint amongst men. I was honestly confused about why they came to me. I thought, 'You can't be serious! You chose me out of everyone you could have gone to?' Then I found out that Nelson Mandela was into The Wire. I thought, 'It's amazing – he might have kicked back and watched the Wire box set!' The role was definitely the biggest challenge of my life. I look and sound nothing like the man – but hopefully I've pulled it off."

In addition, Elba recently made his debut as a writer-director with The Pavement Psychologist, a half-hour drama about homelessness for Sky Arts. He also somehow squeezes in a successful parallel career as a DJ operating under the moniker of DJ Big Driis.

But for the time being, Elba is once again burning up the screen in the title role of Luther, the most magnetic British TV cop of his generation, which returns soon to BBC1 for a highly anticipated third series.

In person, Elba exudes the same charisma as Luther – it radiates from him like a sci-fi movie force-field. He possesses the most important, yet most elusive quality for any actor: sheer presence. Dressed in a light magenta shirt, dark tie and trousers, the actor is an imposing, impressive figure who dominates the room both literally and figuratively. It is no surprise to learn that he was named the third sexiest man alive in a recent People magazine poll. When I mention this to Elba, he goes all shy on me. "Was I in that poll?" he smiles coyly. "Luther would hate that. He's supposed to be tough, not some guy in a sexy T-shirt. But it's a compliment, I guess," he says, before adding with mock exasperation, "even though I only came third!"

It is also quite easy to see why Elba has been touted in some quarters as the next James Bond, a story which he cheerfully laughs off. "It's just a rumour. But what a compliment that my name has been attached to that role! Of course, it's not my job – it's very much Daniel Craig's – but I'm flattered by the notion of it. I'm also encouraged that audiences are being more colour-blind these days. If people are associating me with such a job, I think that's great."

So with all this heat that he has been generating, it is a relief to report that Elba has managed to fit into his schedule four more episodes of Luther, surely the coolest cop show around. In Neil Cross's darkly brooding series, Elba plays DCI John Luther, a detective more haunted than a fairground ghost train.

The first two series gained a huge worldwide following and won Elba a 2012 Golden Globe award for best actor. The critics were equally enamoured of this intense, sometimes outlandish, but never less than compelling series. Slant Magazine, for instance, commented that Elba, "barrels through it, creating the most watchable TV detective since Helen Mirren's Jane Tennison on Prime Suspect."

Part of Elba's appeal lies in the fact that he displays great economy on screen – he can express more with one movement of an eyebrow than lesser actors manage in an entire movie. He is from the "less is more" school of acting. In the first episode of the new series, Luther is even more disturbed than usual. He is tugged in many different directions as he simultaneously chases both an unhinged fetishist who is carrying out brutal copycat killings on women and the murderer of a vicious internet troll.

At the same time, Luther is obliged to deal with an enemy within who is attempting to turn his closest ally, his colleague DS Justin Ripley (Warren Brown), against him. As if he didn't already have enough on his plate, the perennially troubled 'tec is also bouleversé by the appearance of a charming new girlfriend (Sienna Guillory).

So just what is it that makes Luther stand out from the crowd of TV cop shows? One explanation is that the show is an unapologetically tough watch. This is a detective who thinks nothing of hanging a suspect by one arm over the edge of a skyscraper walkway in pursuit of answers.

The show is driven by Luther's burning desire to right wrong. He is a character who can never rest easily; he is propelled by a permanent ache of dissatisfaction that there will always be bad people doing bad things.

Elba explains the character's motivation. "I watched a good documentary the other day which dissected what makes different people happy. Luther and I share the idea that you can never be too happy. I recognise that, for sure. You can't be too happy or something is wrong!"

The evangelical fervour with which Luther hunts down villains makes for an unrelenting viewing experience. The 35-year-old Brown, who has also starred in Good Cop and Occupation, recollects a moment during the shoot which underlines the unremitting nature of the show. "We were filming this dark scene in a graveyard in east London. I said to Idris, 'This is really depressing. I'd love to do some comedy!'

"I adore getting my teeth into a role like this and baring everything – that's why you do this job. But you can't do it on every production or you'd go mad. Sometimes you think, 'God, I've been looking at a dead woman in a freezer all day!'" Welcome to the world of Luther.

But do the cast ever worry that, in its uncompromising depiction of brutality, the show risks overstepping the mark? Elba, who is also a producer on the programme, believes it is vital not to soft-pedal the horror Luther has to confront on a daily basis.

He reflects that, "TV has to be responsible for what it puts out there. For instance, Good Cop was taken off air because it mirrored a real-life crime. You wouldn't want to go too far because it goes into people's homes. That's me with my producer's hat on.

"The violence on Luther has been something where we all say, 'Ooo, can we go further?' But of course we can go further, because we know Luther will make the villains pay for their crimes. Neil will show you something really horrific, but, boy, will you then want Luther to catch the bad guy. That's the payoff. We stretch the depths of how dark we can go just so we can show you how heroic and just Luther can be. I think we have managed to do it in a way which allows viewers to celebrate Luther's win at the end. They appreciate his triumph in catching someone who's done something awful."

Brown chips in that, "People ask, 'Is this too much?' I don't think it is. It's great that people talk about it. But we're never shocking for shocking's sake. The drama is heightened, everything is pushed to the limit. It's certainly not a comedy!"

Another reason for the show's popularity may be the fact that it is morally ambiguous. Luther is a cop who has to do the wrong thing for the right reasons. For him, the law is often as much a hindrance as a help.

Brown observes that, "In the past, detective shows were quite clear-cut – 'Right, this is someone who needs to be taken down'. But Luther is more morally complex. It treads a fine line and asks, 'What would you do in that situation?'"

Guillory, 38, adds that this moral complexity helps distinguish Luther from more run-of-the-mill TV 'tecs. "It's simply not like anything else. It's The Dark Knight crashing into every police procedural you've ever seen. It rips the conventional cop show apart and turns it into a revenge thriller. Nasty things happen along the way, but that's one of the reasons why it's so good."

Elba, who has a 10-year-old daughter, Isan, by his ex-wife, the Liberian actress Dormowa Sherma, is now in the happy position of being able to pick and choose his roles. The only problem is fitting everything in, a difficulty he overcomes with enviable reserves of creative energy.

The actor, who began his career training at the National Youth Music Theatre, courtesy of a £1,500 grant from the Prince's Trust, is quick to credit The Wire for kick-starting his success. "I would not be here without The Wire. My career would not be what it is without that show. Even though it ended five years ago, people still approach me in the street to give me compliments about it. It has really stuck in their minds.

"It had such depth of characterisation. Audiences want that – they are smarter now. Gone are the days where we wanted to be spoonfed. The Wire forced viewers to think, and that's why it was such a success."

So does Elba, whose father worked at the Ford factory and whose mother was a clerk, see himself as a role model? "I'd like to think so – not necessarily by giving talks, but by my actions. I'd also like to think that people from outside my community could take inspiration from what I've done. I'm very satisfied with how things have gone. Ten years ago, I'd never have imagined doing all this.

"Yesterday I was called a 'cultural icon'. How did I react to that? I laughed loudly and said, 'What?'"

'Luther' starts on 2 July at 9pm on BBC1