Talking to David Mitchell and Michel van der Aa feels a little like butting in on a date. The Man Booker-shortlisted novelist and the Dutch composer have written an opera together, Sunken Garden, to be premiered by English National Opera next month. But even that stressful experience seems not to have soured their mutual admiration, which flips affectionately between them, batted back with a cheerful "Get out of here!" from Mitchell or "Enough of the compliments!" from Van der Aa.

Mitchell says their first meeting was a bit like a "speed date". The initial approach came from Van der Aa, winner of a Grawemeyer (the composing equivalent of a Nobel prize): he wrote to the author of Cloud Atlas and Black Swan Green, suggesting that they collaborate. "Good art and good music always find a balance between form on the one hand, and poetry and human feeling on the other," he explains. "Bach may be the prime example, and I found something similar in David's books. But I never expected to hear back from him." One day Mitchell was at a loose end in Amsterdam, and mentioned Van der Aa's email to his Dutch publisher. "I almost didn't – it was one of those Garden of Forking Paths moments." The next thing he knew, he was sitting in a cafe with Van der Aa.

"We were like two dogs warily eyeing each other up," says Mitchell. Van der Aa adds: "We talked a lot about opera and what opera should and shouldn't be. We talked about the building blocks for an opera: what is a text that invites itself to be sung. And we somehow got chatting about The Wire and Twin Peaks" – shared obsessions, as it turned out.

The idea for Sunken Garden gradually grew. Cloud Atlas was being adapted for film at the time, so they met at airports when Mitchell was shuttling between LA and his home in the west of Ireland. "David would just be on his way back to Cork from a read-through with Tom Hanks."

The novelist had already written one libretto, for Dutch composer Klaas de Vries, about the 2000 Enschede fireworks disaster, and says he enjoys breaking with the utter solitude of the novelist's life. "You work on something for basically four years without speaking to anyone and you get lonely." Opera is the opposite, the supremely collaborative artform. "No one person could begin to do this space-programme-sized project without a host of other people. And it was like playing table tennis with Michel when we were developing the libretto. You'd knock him an idea and he'd send it back with some crafty topspin, and you'd put some backspin on to counter, and each time the manuscript got handed over it got better."

The narrative, which Mitchell describes as "an early offshoot of what my next novel might have been", has something of the film noir about it. (The pair describe it as "an occult-mystery film opera".) Toby Kramer is a filmmaker investigating the disappearance of a software engineer, Simon Vines. His quest leads him to the sunken garden, a liminal place between life and death, where he meets psychiatrist Iris Marinus. (Mitchell's readers will recognise Dr Marinus from The Thousand Autumns of Jacob de Zoet.) There are hints throughout of Mitchell's novelistic preoccupations: the relationship between the body and the self, incorporeality, immortality, fate.

Van der Aa works in an unusual, if not unique, way. Sunken Garden is his third opera, and, like his last, After Life (based on the film of the same name by Hirokazu Koreeda), it will meld music and his own film; he also directs. Of Sunken Garden, he says: "I wrote what I felt worked best with the libretto to bring it to the audience. Sometimes that means soundscapey stuff, but also, sometimes, in-your-face dance music and electronic music, or pop music, almost. It's a very kaleidoscopic score with a very broad range of expression. And I sometimes use very realistic, documentary-style film, and sometimes very abstract film, and everything in between – it's all in service of the story." He has used 3D film to create the sunken garden of the title: lush, colourful footage shot at Cornwall's Eden Project. "It earns its place, or else it would just be a gimmick," Mitchell says.

Why opera as a vehicle for telling this story? For Mitchell, it means abandoning control – letting actors, singers, designers, a conductor and musicians do much of what he would convey in words in a novel. He laughs, saying that he can see that his importance is dwindling "the closer we get to launch date, or what is it? Premiere. This is what I call the storm dilemma. When you write a storm in prose, you do everything. You need some fresh metaphors to do the noise; you have to do two pages to make it really stormy. In a screenplay or libretto you just write 'storm'." (He gave the same reason when asked in a recent Guardian interview why he had not adapted Cloud Atlas for film himself: he didn't want to be the guy who wrote "storm".)

Van der Aa chips in. "The converse is that he writes two words in his libretto, 'vertical pond', and it costs thousands of pounds to make it. Two words and it's like, ker-ching! People have been working for weeks on inventing the vertical pond in the visual effects department."

So, notwithstanding the "storm dilemma", what can opera do? "It's the human warmth," says Mitchell, "the fact that these are humans just like you, singing this stuff. There is something sacred in the human connection between the performers and the audience. They could screw up, or fall over – it's a high-wire act. There's a tensile cord between you and the performers that's only there when it's in real time, when real human beings are producing these extraordinary sounds."

That argument works for theatre, too: why add music? Van der Aa argues that "music has the possibility of being non-specific. Music frees you from realism. You can leave the distance between the audience and the subject of the piece slightly bigger than in film."

Mitchell excitedly expands. "There's a spectrum in art, with specificity at one end and ambiguity at the other. Fiction is at the ambiguous end. Take the characters in Cloud Atlas. There are as many ways of seeing the characters as there are readers – until it's filmed. I know that my Timothy Cavendish will never be anyone other than Jim Broadbent, and Jim Broadbent's Timothy Cavendish is even there in my next book. Theatre has something of this quality: this room looks like this, this character looks like this. But music is on the ambiguous end."

Anyway, they say, what kind of a question is that: why opera? "It's rather Anglo-Saxon," says Van der Aa. "In Europe, people don't question that you spend quite a bit of money on opera." Mitchell says the question reminds him of hearing another novelist, Howard Jacobson perhaps, being asked "What is literature for?" at a festival. The answer came back: "What a delightfully childlike question. You may as well ask: 'What is the moon for?'"