When Luther first aired on BBC1 in 2010, critics were sniffy about what they perceived to be its broad-brushstrokes approach to cop drama. The Telegraph said it was "formulaic"; the Guardian called it try-hard. It may have had Idris Elba as its moody, brooding lead, but the kind of acclaim that greeted The Wire was not forthcoming. Ratings dropped off as the series went along. A recommission looked unlikely.

In the three years since then, Luther has not only survived but flourished, slowly and surely becoming a bona fide cult hit. Back in February, a teaser confirming a third run with a sketchy graphic of Elba looking intense was enough to send fans into a frenzy. So here I am, on the set of series three, watching Elba run through his lines in that trademark heavy jacket and red tie. He's polite, but not particularly chatty. Later he will explain that people steer clear of him on set. "I end up being quite darkened, mood-wise," he says. "I saw a man hanging from a tree. I've never seen that in my real life. I know it's a stuntman, but the impact of that... it's a very dark show."

Luther is dark, but it's also fundamentally odd, which may be why it took time to embed itself in viewers' minds. On paper, it reads like a straightforward police procedural. There's a grisly murder, the workaday investigators are stumped, then maverick DCI John Luther comes along and solves it with his finely honed instincts. There's some moral ambiguity – he'll rough up crims to get what he wants, he's not a very good husband, and his most trusted ally is a patricidal psychopath – but in theory, there's little to differentiate it from, say, Prime Suspect or Cracker.

Yet it is different. The shooting script for today's scenes is titled "Alice's Lair", and that word is a considered choice. Alice Morgan – said patricidal psychopath, played with delicious wickedness by Ruth Wilson – is one of TV's most unusual sidekicks. She's half mad scientist, half Veronica Lake. That she has a lair (even if it's a nice penthouse flat overlooking Shoreditch Park, rather than a gloomy cave) says something about the show's taste for comic-book stylings.

Its visual flair is part of what makes Luther so scary. It looks like the stuff of nightmares. It has a knack for tapping into common fears with cases that play out like urban myths. There's a killer who attacks at random, wearing a gruesome mask and knocking on doors until some sorry victim makes the unfortunate decision to answer. There's the satanic bogeyman who charms his way into women's houses, then licks their faces before imprisoning them in a freezer. It's often so baroque that it borders on the absurd.

I ask Warren Brown, who plays Luther's partner, Ripley, if he ever thinks the show goes too far. "I do often think, 'What's going on in your head, Neil?'" he laughs, referring to Neil Cross, the show's creator and writer. "Although it's naturalistic, it's very heightened. It is comic-book. We do push the boundaries. I love that about the show. It's one of the things that makes it stand out."

'Luther plays like a film, like an American show. They're not seeing 'stiff upper lip' TV. They're actually seeing this ballsy, fucking six-foot tall black guy kicking some arse'

Photograph: Steve Neaves

Elba says that this boldness has helped Luther translate to an international audience; he was nominated for a best actor Golden Globe in 2011, and won it a year later. "The audacity of the show is what really appeals to Americans," he explains. "Luther plays like a film, like an American show. They're not seeing 'stiff upper lip' TV. They're actually seeing this ballsy, fucking six-foot tall black guy kicking some arse. If it's on, you'll end up watching, because you'll see some bizarre shit you haven't seen before."

It may have blazed a trail for "bizarre shit", but in Luther's 18-month absence, terrifying TV has become far creepier, and far more common. This year, we've already had Utopia burning that chilli scene on to our retinas, and Jamie Dornan shredded nerves just by standing at a window in The Fall. So can Luther maintain its menace with other gruesome dramas snapping at its heels?

Series three opens with a jumpy trick that deftly, confidently swats away the competition – and it only gets weirder from there. There's a killer on the loose who likes to dress his victims in black clothes and shredded tights. They call him the Shoreditch Creeper and ascertain that he's a Siouxsie & The Banshees fan. Luther and Ripley then proceed to bicker over what genre the Banshees are: "Post-punk." "Goth?" "Post-punk." It's funny. Without these flashes of self-awareness, Luther would indeed be too much. The knowing tone redeems it.

Sienna Guillory, who plays Luther's new love interest, Mary Day – surely a thankless role, given what usually happens to the people who get tangled up in his life – has her own theories as to why people love the programme. "It's a graphic novel revenge tragedy," she offers, before suggesting it's the appealingly zingy dialogue that sets the show apart. "All the women have a completely different vernacular, and they bring that out in Luther. Then there's this wonderful, cracking, audacious dialogue between Luther and Alice. Neil Cross is brilliant."

There's a clear sense of finality running through this third series, so what this means for Luther's resurgent love life is anyone's pessimistic guess. Finally, Cross has realised that even in a hyperreal, comic-book world, policemen can't ring up the number of bodies that Luther does and continue to get away with it. He's lost his wife and his best friend, and countless criminals have expired on his watch. He's been in trouble and on the run. He may be morally straight, but he's professionally bent. Yet up until now, he's remained a serving officer.

The main story arc of the new season suggests that time is running out for Luther's less-than conventional working methods. Ned Dennehy (Tyrannosaur, Parade's End) joins the cast as a recently un-retired officer charged with weeding out corruption in the force, assisted by Luther's one-time colleague and now foe, Erin Gray. They plot to hit him where it hurts by turning Ripley against him. If the strategy's a success, it could mark the tragic end of a solid bromance. Sweetly, it seems that Brown and Elba are close in real life. "I was a massive fan of The Wire," reveals Brown. "I think I actually had the theme as a ringtone for a bit. Then I got a call: 'You've got Luther.' Great! That's the ringtone off."

'The film will be more interesting to make. We think we're making a film when we're making our show, so I think we should go all the way'

Idris Elba as Stringer Bell in The Wire

On set, cast and crew are clearly relieved to be nearing the end of filming. They're on a particularly tight schedule, even by TV standards, and they're contending with all the icy-drizzle joys of shooting in London in February. It is likely to be the last time they have to do so, at least for the small screen.

"If I'm honest, yeah, it might be the end of the TV show," says Elba. "As far as another series is concerned, I don't think we're going to do any more."

In many ways, Luther's key players have outgrown it. Ruth Wilson went to Hollywood shortly after series one, and only briefly appeared in series two, though such is Alice's popularity that there has long been talk of a spin-off vehicle for her character (still, sadly, unconfirmed). Neil Cross has also gone Stateside, creating a new drama based on the life of the pirate Blackbeard, called Crossbones. Then there's Elba, who has gone from post-Wire lull to blockbuster star, with roles in Prometheus and Thor, and an upcoming stint as Nelson Mandela in Mandela: Long Walk To Freedom. He acknowledges that a lot has changed since he first signed up to play the east London DCI. "Even though I was popular from an American show, British audiences hadn't seen me on TV in at least 10 years," he says. "It was a risk taking me as the lead of the show."

It paid off, and although this may be the end of Luther as a BBC TV drama, there's life in the old cop yet. Cross has already written one Luther novel, 2011's The Calling, and Elba is working with Cross on developing a Luther movie, having already worked behind the scenes as producer this time around.

"The film will be more interesting to make," reckons Elba. "We think we're making a film when we're making our show, so I think we should go all the way." Besides, this mad dystopian crime opera has already left its mark. These days, people in the street no longer call Elba Stringer Bell. They call him Luther.

Luther starts in the UK on Tuesday, 9pm, BBC1

LUTHER: THE SERIES THREE LINEUP

John Luther

Gruff of voice, red of eye, natty of coat, the maverick DCI is good at solving crime, bad at life.

Alice Morgan

TV's favourite psycho sidekick returns to help/hinder Luther's latest investigation.

Justin Ripley

Luther's loyal young partner and fall guy. Back for more despite a nasty torture episode last time.

Martin Schenk

Luther's quietly shrewd boss, responsible for re-employing him, despite endless cock-ups.

Mary Day

Vintage clothes saleswoman (hey, it is east London) who becomes Luther's new love interest.

Benny Silver

AKA Deadhead – DCI Luther's dope-smoking, Warcraft-playing, prog-loving tech support dude.