Early last year, playwright and screenwriter Jack Thorne took a call from an old acquaintance offering him work.

"I almost bit his hand off," he laughs. If Thorne had left teeth marks, it would have been appropriate: the caller was Tony Award-winning theatre director John Tiffany and he wanted the 34-year-old Bristolian to pen a stage adaptation of John Ajvide Lindqvist's 1980s-set novel Let The Right One In. The story turns on the friendship between 12-year-old Oskar, a lonely, bullied schoolboy, and Eli, an equally lonely girl who happens to also be a centuries-old vampire.

If you haven't read the English translation of the book, you may have seen Tomas Alfredson's critically acclaimed Swedish film version. You may even have seen Let Me In, Matt Reeves's faithful Hollywood remake, which transposes the action from the dreary Stockholm suburb of Blackeberg (Lindqvist's birthplace) to the town of Los Alamos in New Mexico. And if you're really keen on the world of Oskar and Eli, you'll know there's also a US comic book revamp which deals with Eli's back story and which has been disowned by Lindqvist.

Thorne's stage version is for the National Theatre of Scotland (NTS) and is set in the city in which it opens on Wednesday – Dundee. The play draws on both the original novel and the films, but necessarily adds a few flavours of its own to reflect its transference to the stage, and also the very particular predilections of its adaptor.

"John knows exactly what I'm drawn to, so he would have known I was a fan," Thorne says simply when I ask him why it was his number that Tiffany dialled last year. "Let The Right One In is about self-hatred and loneliness, so I'm the right writer for that."

Take a look at Thorne's CV and you can see how true that is. As well as writing several plays for stage and radio, he has written for dark teen television drama Skins, collaborated with Shane Meadows on the scripts for This Is England '86 and This Is England '88 on Channel 4, created his own Bafta-winning supernatural mini-series for BBC Three, entitled The Fades, and written a screenplay, The Scouting Book For Boys. Outsiders and loners feature in most of them and The Scouting Book For Boys has a similar awkward-boy-meets-awkward-girl coming-of-age plot to the one in Let The Right One In. But without the gushing blood.

But even Tiffany couldn't have guessed how much of a fan of Lindqvist's work Thorne was when he picked up that phone, however. "I'd seen the Swedish film three or four times, and I'd seen the American film as well," the writer reveals. "I tend to watch and re-watch things that I love. I'm built that way."

However, what Thorne hadn't done at that point was read the book, so that was his first task when he accepted the commission, which was to be co-directed by choreographer Steven Hogget (who won an Olivier Award in 2009 for his work on the NTS's massive hit, Black Watch). He also read some of the many academic papers which have been written about both novel and film.

"The book gave it a lot more shading," Thorne says. "It shades in areas you don't want shading in, such as Hakan's character [Eli's guardian, whose role is left deliberately ambiguous in the film], but Oskar's family was something I really seized upon. So I could give more depth to that and to his being bullied, and in particular the journey of Oskar's early sexuality. So there were lots of new nuggets of information about him which really helped."

The American film version likewise tackles Oskar's sexuality – to the point where Reeves added an early scene in which Oskar spies on his neighbour getting dressed. But the other changes are minimal, making Reeves's version not a re-imagining but a good old-fashioned remake. Stephen King called it "a genre-busting triumph - the best American horror film in the last 20 years" and Thorne is equally fulsome in his praise, if a little less wordy. "Bloody good," he says simply.

Alfredson was initially asked to helm the US version but turned it down, saying he had no interest in telling the same story twice. By that point he was also involved in the film version of Tinker, Tailor, Soldier, Spy – another piece about a lonely outsider. But the producers of the Swedish film also worked on Let Me In, and Reeves worked from the screenplay Lindqvist had written for Alfredson.

For Thorne, then, the process of adapting the story for the stage has required him to draw on his own preoccupations, on John Ajvide Lindqvist's source material – both novel and screenplay – and on the filmic visions of Matt Reeves and Tomas Alfredson, who is one of European cinema's most stylish and precise directors.

As well as taking all those influences and triangulating a point between them in which a theatrical production can sit, he has had to factor in Dundee, a city he had never visited until recently. "I did a lot of Googling about Dundee to try to get a sense of it before I wrote the first draft," he says. "It's quite a Swedish place, which is why John went for it. It has a sort of Swedish feel."

Meanwhile, 15 miles away in Kirriemuir, a statue recalls the most famous creation of an author and playwright whose work also casts a shadow over this Scottish take on Let The Right One In: Peter Pan. "It's a very much darker sort of Peter Pan, but it's about growing up and what you do to survive growing up, in the same way that Peter Pan is," Thorne admits. "And it's also about staying young when everyone else is growing old, which is a tragedy."

So, what can a theatrical adaptation of Let The Right One In give us that a novel and two films can't? What will it add? "Good theatre is about a discussion between the audience and the stage which cinema doesn't do to the same degree," Thorne says. "And the lyricism of what we were trying to do is also very different. A Steven Hogget and John Tiffany production will not be a retelling – it will be a lyrical, beautiful thing and one of my jobs as a writer was to leave enough space for that. So I kept it very spare and very simple."

To that end, Thorne cut away some of the subplots and concentrated almost solely on the scenes between Eli (played in the NTS production by 24-year-old Rebecca Benson) and Oskar (played by 18-year-old Martin Quinn, in his first professional role).

"I really wanted to spend as much time as possible with Oskar and Eli, so those scenes last longer than they do in either of the films or in the book," Thorne explains. "They're very much about two inquisitive kids trying to get to know each other. And I've given a lot more context to Oskar's world so that you spend a lot more time with him, with his family, with the bullying. Focussing in on those two was the really important thing."

In fact, Thorne's isn't the first stage version. In 2011, the Uppsala Stadsteater in Sweden premiered actor-director Jakob Hultcrantz Hansson's take on the novel. The NTS production is greater in both scale and ambition than the Swedish version, however. Tiffany and Hogget previously worked together on The Bacchae, an NTS production which starred Alan Cumming and later transferred to New York, and on Broadway hit Once, adapted from the film of the same name by Irish playwright Enda Walsh. And of course they made a sensation of Gregory Burke's Black Watch, turning the NTS production into globe-trotting theatrical tour de force. Let The Right One In is another potential blockbuster.

For the music, meanwhile, Tiffany has enlisted Icelandic composer Olafur Arnalds, who scored recent ITV hit Broadchurch and, finally, New York-based effects designer Jeremy Chernick has been hired to make sure that when a neck is punctured the arterial spray looks real. Eli is a vampire, after all – and even on stage, vampires need to drink blood.

For Jack Thorne, however, all that comes under what he calls "bells and whistles". For him, it's in the intensity of the relationship between Oskar and Eli that the power and the beauty resides. "Imagining those two sitting on a climbing frame, on stage, talking – I just think that's so theatrical and brilliant."

On Wednesday, we find out if he's right.

Let The Right One In opens at Dundee Rep on June 5 and runs until June 29