When Green Room's world premiere took place at the Cannes Film Festival a year ago, it was as if writer-director Jeremy Saulnier had hard-wired the seats with 50,000 volts. Not since The Blair Witch Project played at the festival – in the very same cinema, in the Director's Fortnight strand – had there been so many screams and sweaty palms. For a festival crowd reared on rarefied arthouse movies, this gritty tale of a punk band in a deadly stand-off with a gang of neo-Nazis was classic counter-programming.

It's been terrifying audiences – including at this year's Glasgow Film Festival – ever since. 'This is the kind of movie where there's no choice,' argues Saulnier, when we meet in London. 'If you buy into it, you're sucked in and you're dragged through this experience…you have to experience it and survive it and it's really fun to get caught up in that and let go of your intellect. Let's just survive this experience together and then have this sigh of relief when you emerge from the theatre.'

It begins when low-fi punk outfit, the Ain't Rights (Anton Yelchin, Alia Shawkat, and Britain's Callum Turner and Joe Cole), arrive at a remote rural Oregon bar to play a gig. The extreme right-wing crowd becomes hostile when the band opens with a cover of the Dead Kennedy's ‘Nazi Punks Fuck Off'. But the terror really starts backstage when they witness a murder. Facing off with the bar's pragmatic owner Darcy (Patrick Stewart) and his merciless crew, the Ain't Rights are soon fighting for their lives.

While it's shocking to see the genial Sir Patrick Stewart – he of Star Trek and X-Men fame – playing a vile villain, Darcy feels like a negotiator at times. Without giving too much away, he has more business interests that just his bar and the electrical repair business advertised on his van – something he wants guarded from any potential police murder investigation. 'Gradually, you begin to realise that's a terrifying situation and no way are these kids going to be allowed to leave,' says Stewart.

What follows is an hour or so of pure heart-pumping adrenaline – a survival scenario that goes from bad to worse to extreme. 'Why do these kids make a lot of decisions that they do?' asks Yelchin, rhetorically. 'Because they're fucking twenty-something and they're stuck in a room and told they're going to get murdered! They make weird choices. They try to think their way out of things and they can use their ingenuity to a certain extent, and they just fail – we're just humans. I find that moving.'

For Saulnier, who made his name with the much-admired 2013 revenge thriller Blue Ruin, the film has a hugely personal side. Hooked on punk from the age of 9, after hearing the Dead Kennedys' 1980 debut, Fresh Fruit for Rotting Vegetables, he spent his youth in various hardcore punk bands in suburban Washington DC. 'The first show [they play] in the movie is modelled after a show I actually played at a Mexican restaurant,' he chuckles. 'It was this really sad show. No-one turned up!'

Using songs written by local bands from his adolescent years, re-recorded for the movie by Portland-based band Toxic Holocaust, Saulnier insisted the actors learn how to play them. 'We got to rehearse all the time,' says Shawkat (best known as Maeby from Arrested Development), who played electric guitar in the film. 'We really felt like a band. We had a recording that we would play to, but we played all the songs several times…at the wrap party, we even put on a whole live show for the crew.'

Some were total newcomers – Peaky Blinders star Joe Cole had never touched a drum-set before – while others went deep. 'Callum became obsessed with Johnny Rotten,' recalls Saulnier. 'He would dress up in this coat and walk around London, trying to get into this character.' Stewart, meanwhile, researched into the neo-Nazi sub-culture prevalent in the Pacific Northwest, studying what he calls 'the insanity of it all, the delusion, the craziness, the lies, the wanting to turn the clock back to some other time when fascism was the only solution'.

When it came to the shoot, it was 'exhausting', says Yelchin, who spends a lot of the film wrapped in bloody prosthetics and yelling in pain. 'It was draining for everyone!' Shawkat, whose role was originally written for a male, concurs. 'We were all in very dark states,' she says. 'It was like shooting two different films. The beginning part, all of us like a band, just hanging out, and then a very high-energy and emotional drama.'

Even Stewart, who wasn't in Cannes for that first screening, was 'completely unprepared' when he finally saw the finished movie play in the Midnight Madness strand at Toronto. 'To see a cinema audience transform into a soccer crowd…I'd never seen an audience behave like that, shouting out, yelling, screaming, gasping, applauding when something bad happened to somebody they didn't like!' he smiles. 'It was unsettling!' You have been warned.

Green Room opens on 13 May.