British TV audiences don’t, as a rule, like subtitled foreign drama, but Danish crime series “The Killing,” in which a single crime is investigated over 20 episodes, has proved an exception to that rule.

AMC has just remade the series in English, with an April 3 premiere in the U.S., but in Blighty, the original version has become a cult hit, attracting audiences of 520,000 on upmarket digital channel BBC4 while eliciting rave write-ups in the press. Its ratings compare favorably with “Mad Men,” which attracted 470,000 on the same channel a few months ago.

BBC acquisitions head Sue Deeks, who picked up “The Killing,” is clear about the reasons for its popularity.

“It is just a very gripping drama,” she says. “It is complex, and because the story is told across 20 episodes it gives you time to get to know the characters. Also, it’s not just about the hunting of the killer, it is about the human cost of the tragedy.”

Piv Bernth, who exec produced the show for Danish pubcaster DR and developed it alongside writer Soren Sveistrup, agrees: “It’s not only about finding out who the killer is. We are telling a story about people and the impact these events can have on their lives.”

BBC4 has gradually built an audience for foreign-language drama that did not previously exist. This began when it started to air French crime series “Spiral” in 2006, followed by the Swedish version of “Wallander” in 2008, which was helped by the popularity of the English-language version of the drama, starring Kenneth Branagh.

Like “The Killing,” the Swedish “Wallander” built a cult following on BBC4, attracting audiences of up to 480,000.

Both “Wallander” and “The Killing” have also benefited from the success of “The Girl with the Dragon Tattoo” film trilogy, which helped cement Nordic crime drama’s reputation for quality and intelligence.

Ole Sondberg, exec producer for Sweden’s Yellow Bird, which produced both “Tattoo” and “Wallander,” is struck by how the U.K. market has changed in such a short time.

“Only a few years ago, the very idea of selling a Scandinavian program to the BBC was just unthinkable,” he says. “It never happened.”

Alexander Coridass, president and CEO of ZDF Enterprises, which co-produced “The Killing” and reps the series in international markets, agrees.

“The Anglo-Saxon markets have traditionally been challenging for programs that are not shot in English,” he says. “That’s why we really appreciated it when BBC4 had the courage to offer it to its audience, but it just goes to show that if you take that risk, it can work.”

Bertrand Villegas of TV consultancy The Wit says that the success of Nordic series has been driven in part by the popularity of Scandi crime novels, which have a reputation for complex plots and nuanced characterization. The series and films have reinforced this and are now seen as upmarket fare for educated folk. “It is an image of quality,” he says.

One factor that has helped develop the market is the growth of niche channels, such as BBC4, dedicated to an upscale audience, who are used to watching foreign-language fare in their local arthouses, Villegas says.

Another development that has helped sophisticated dramas like “The Killing,” with their interweaving storylines that continue throughout the series, is the development of catchup TV services, like the BBC’s iPlayer. These have allowed audiences to build through word of mouth, with new converts watching past episodes back-to-back in the same way they would with a DVD box set, immersing themselves in the atmosphere of the drama.

“It’s like reading a good book,” Bernth says.

Another strength of these dramas is their strong, distinctive protagonists: Sarah Lund in “The Killing,” Lisbeth Salander in “Dragon Tattoo” and Kurt Wallander in “Wallander” are both very human in their faults and frailties, but also fiercely independent and unconventional — yet entirely believable.

Bernth says that they gave Lund many of the characteristics usually ascribed to a male detective — laconic, driven and self-contained — whereas her male sidekick displays the traits often give to a female character: He cries, frets about his family and so on.

But to carry off these role, the actors also have to be top-notch, and the Nordic dramas have been carried in part by the superior acting of the leads — in the case of “The Killing,” a stellar turn by Sofie Grabol as Lund. (Mireille Enos of “Big Love” has the role in AMC’s version.)

Rikke Ennis, CEO of sales company TrustNordisk, is now seeing the benefits of the Nordic crime wave lift the prospects of other Scandi films and series, such as the upcoming adaptation of Camilla Lackberg’s series of novels, “The Fjallbacka Murders.”

While Scandinavian crime drama has traditionally had a strong following in Germany, now other markets — such as the U.K., Spain and Italy — are opening up to it, Ennis says.