When she first saw John Adams's opera The Death of Klinghoffer in the early 1990s, Penny Woolcock admits that she had almost forgotten about the incident that inspired it: the hijacking of the Achille Lauro by Palestinian terrorists in 1985. It was an incident that yielded a macabre, iconic moment. Before giving themselves up, the terrorists murdered Jewish-American tourist Leon Klinghoffer. "I remember there was this guy in a wheelchair they had killed and thrown overboard," she says. "Then there was the trial of the Palestinians in cages in Italy."

Woolcock's film version of Adams's opera received its European premiere at the Rotterdam festival earlier this month, following its screening in Sundance a few days earlier. It's a bold and dynamic attempt to open the work up for the big screen. The director confronts the maelstrom of Middle Eastern politics head on. She includes archive footage of the Sabra and Chatila massacres, Holocaust sequences, brutal scenes of a woman being stoned set in present-day Gaza, and a recreation of the razing of a Palestinian village in 1948. She also accentuates the thriller elements of the story, with passengers hiding in their bathrooms.

How do you make opera cinematic? The trick, says Woolcock, is to avoid a stately, theatrical approach: shoot the film handheld, record the sound live, and - above all - cast singers capable of acting. The singers she recruited for Klinghoffer were a little surprised when she sent them off to do Kalashnikov training or to learn about life in a wheelchair, but they took her unconventional methods in good heart. The result is dynamic, naturalistic performances.

There is nothing static about Woolcock's mise en scène either. While staying true to Alice Goodman's libretto and Adams's music, she cut choruses, added dialogue and even introduced new characters (for instance, the Holocaust survivor passenger we see in flashback taking part in the eviction of Palestinians from their homes). "The original production [by Peter Sellars] was very abstract," she says. "The singers all wore the same clothes. You couldn't distinguish the hijackers from the hostages. The most sadistic of the hijackers also played the ship's captain." The film needed a more conventional narrative arc.

The story of how a little-known film-maker from the UK came to collaborate with California-based Adams, one of the most celebrated living composers, is intriguing. Although heralded as one of the bright young hopes of British cinema, Woolcock is, in fact, a 53-year-old, Argentinian-born single mother. She was brought up in the suburbs of Buenos Aires in an ex-pat community where her father was an accountant. Desperate to break away from her middle-class roots, the teenage Woolcock joined a theatre group whose motto was: "Liberty and Intoxication!" She was arrested during the military dictatorship, fell in love with a young working-class guy and ran away from home. "Suddenly I was 18, living in Barcelona, and I had a baby and I wasn't married. I went from a very uptight, regulated life to being right on the margins - and skint."

After splitting up with her partner, she came to the UK, and has been here ever since: "I spent 15 years either on social security or doing menial jobs." She was nearly 40 when she was "discovered" by Channel 4 as a result of Macbeth on the Estate, a low-budget film she made about a project to perform Shakespeare on an Oxford council estate.

Woolcock was halfway through writing her Bafta-nominated TV drama Tina Goes Shopping when, almost on a whim, she approached Channel 4 with the idea for Klinghoffer. Tina Goes Shopping was set on a Leeds housing estate. Made with non-professional actors, its main character was a single mother who ekes out an existence "stealing to order". Drug addiction is rife, half the residents are in hock to debt collectors and kids cope with the boredom by joy-riding. In other words, a milieu as far away from the world of opera as you can imagine: "I thought they'd say why don't you fuck off, you can't read music, that's not your thing." By chance, though, her proposal arrived just as the channel was rethinking its approach to televised opera. They contacted Adams, who was keen to have a movie made of his opera. "All of a sudden, there was this gust of support. I was thinking, oh my God! What have I done?"

Adams was disappointed that Klinghoffer - picketed when first performed in the US - had had such a troubled life, while his other politically themed opera, Nixon in China, travelled successfully all over the world. Adams liked Macbeth on the Estate, agreed to conduct the London Symphony Orchestra for the Klinghoffer soundtrack, and allowed her to be as radical as she wanted with his material. They cast the singers together: "They needed to have voices, but they also needed to look right - if they spat when they sang, or made funny facial gestures, I couldn't use them." The LSO recording went smoothly, although Woolcock says Adams was startled when she asked him to "up the tempo!"

There was a bigger problem on September 11: "John left a rehearsal to call a cab. He came back in, grabbed me by the arm and said, 'We can never perform this opera again.' He dragged me out and we stood in front of the TV and watched the World Trade Centre collapse."

Adams soon changed his mind. With the music safely in the can, the film crew decamped to Malta, where they hired a cruise liner. Woolcock shot as if she was making an ordinary movie. Speakers were hidden off camera, playing the music "as softly as the singers could bear it" while a conductor gave guidance.

In one bravura sequence, Klinghoffer (Sanford Sylvan) sings a solo as he is spun around on his wheelchair by the terrorists in a sadistic death dance. "He was dizzy and he was on the boat. That affects your voice. I told him I wasn't going to make a fool of him: if he didn't sound right, I wasn't going to use it." Sylvan, who had played the role on stage, attacked the aria, later saying it was the best he had ever sung it.

Ten years after the first stage production provoked fury in the US, feelings about the opera are no longer so heated. Woolcock says she was heartened by how respectfully audiences responded in Sundance. The film will now screen in the US in May as part of a retrospective of Adams's work at the Lincoln Centre and there are moves to show it in Israel. However, it's unlikely to get any sort of mainstream screening in US cinemas or on US television. PBS - the US public service channel - turned it down without even seeing it.

Woolcock is in no doubt why a film that is scrupulously even-handed is still regarded as taboo in certain quarters. "The Palestinians get to say why they're doing what they're doing. Killing a man in a wheelchair is an unspeakable act. But why did they do it? The film asks that question. The Palestinians are given a voice. I passionately believe in the piece and I know it's not anti-semitic. So that kind of criticism, if it comes, won't bother me at all."

As far as her collaboration with Adams is concerned, it seems that Klinghoffer is only the beginning. The unlikely twosome are now considering a new project, one they will develop together from scratch.

· The Death of Klinghoffer will be broadcast on Channel 4 in May.