How do you make Scarlett Johansson disappear? If you’re Jonathan Glazer, a mercurial British filmmaker of singular skill and vision, you do very little. The magic trick isn’t the result of make-up or a disguise, but of context. For Under the Skin, his existential extra-terrestrial 2013 masterpiece, it meant sending Johansson to a Glaswegian shopping centre, where she’d hunt for clothes at Next and ask for help in finding the nearest Asda. It’s the most alien thing about a movie all about one.

The film, regularly chosen as the best British films of the 21st century, is screening at London’s ICA next week (24 October) as part of the Celebrating Free Thinkers festival, marking The Independent’s 40th anniversary. Under the Skin is based on a novel, published in 2000, by Michel Faber. His heroine is an alien with the name of Isserley, who is beamed to Earth from her home planet and tasked with harvesting human flesh, as it’s a delicacy among the wealthy alien overlords she works for. Over the course of Faber’s book, other aliens arrive on Earth and disrupt Isserley’s mission, and she grows disturbed by the ease with which they kill.

Glazer spent years adapting the novel. At one point he made Isserley and a male alien assume the roles of farmers, with Brad Pitt eyed to star. It fell apart, and Glazer went back to work, ultimately stripping Under the Skin for parts. In his final interpretation, dialogue is sparse, explanations are absent, and Isserley becomes nameless, rendered instead a near-silent observer. She still kills, though, feeding her victims to a gloopy black sludge hidden within the ramshackle house she’s taken temporary ownership of. And she still begins to experience feeling, but through the mouthful of chocolate cake she swallows, or the catchy Deacon Blue song she hears on the radio. Glazer’s two previous films – the brutish yet beautiful gangster film Sexy Beast, and the eerie reincarnation tale Birth starring Nicole Kidman – were twisty, plotty psychodramas. Under the Skin is all mood, both sharp with imagination and deliciously inventive in form.

Johansson’s casting in the film was initially guided by finances – a superstar of her stature meant investors flocked to the movie, something that didn’t occur with some of the slightly lower-wattage names (Gemma Arterton and Eva Green among them) attached to Under the Skin beforehand. But Glazer came to realise that Johansson’s presence was eerily perfect for what he was trying to do.

“It made a great deal of sense to cast somebody very well known,” Glazer told The Irish Times in 2014. “I remember seeing her walking along the street in a pink jumper on a long lens and she looks like an exotic insect on the wrong continent.”

“None of us knew how it was going to work,” Johansson told The Guardian that same year. “We toyed with lots of different things like prosthetics, teeth, all kinds of things that would change my face but only slightly, when in fact there was no need to do any of that.”

It creates an uncanny effect on-screen. When Johansson speaks at all in the film – usually to ask passers-by for directions or, beguilingly, say things like “Do you think I’m pretty?” to the men who will be her victims – she has an English accent, something that already makes her stick out in wet-and-windy Glasgow. And then there’s the way she’s filmed at first, via hidden cameras which lurk alongside her. Sometimes people seem to turn and spot her, noticing she looks a bit like the woman from Marvel. Then they go back to their days. Because it couldn’t possibly be her, could it?

Glazer’s approach to the novel was mirrored in his approach to the filmmaking. Another version of Under the Skin might have been more traditional, with actors hired to work alongside Johansson. But Glazer sought experimentation. “We realised it wasn’t about setting up a movie set and having actors pretending to be bus drivers or whatever,” he said in 2014. “Once we put [Scarlett] in that world, we need to be undetectable. We need to film from bird hides. We need cameras in a pot of tea. For the scene in a department store, we had a camera in a mop bucket, one in an umbrella and another up a sleeve.” One hidden camera picked up a couple in the midst of a break-up, which would be observed by Johansson. “It was very beautiful, very sad,” Glazer told Vogue. “And we asked them if we could use the footage, and, of course, they said no. I mourned that one.”

Early in the film, Johansson’s alien drives through central Glasgow in a van, picking men up off the street. The men were real, lured in by the attractive stranger offering them a lift. “They’re all people who just happened to be there,” Glazer told Den of Geek. “It becomes very complicated on one level, from a production point of view, but it’s also very simple on another. You’re not dealing with extras or background action – it’s all live.”

Glazer would communicate with Johansson using an earpiece, suggesting things she ought to ask the men, and calling time on their interactions when he felt he had enough material. Then the men would be dropped off, and Glazer and other members of the production crew – who’d been hiding in the back of the van the whole time – would appear and ask him to sign a waiver allowing them to use the footage. “Some said yes and some said no,” he remembered. “So it was quite wild like that.”

At one point he pondered ditching the rest of the movie entirely, and make Under the Skin nothing but hidden camera footage, like Taxicab Confessions with a brain. “I loved the idea of leaving the door open to reality,” he told The Guardian. “The surprises. The treasure.”

He did, of course, relent, curving the film back towards a bit of a narrative. Johansson’s alien begins to feel as close to humanity as someone of her condition could, becoming vulnerable, awed, admiring. Then, because nothing screams a Glazer film than curdling something fantastical into something tragic, Under the Skin takes a turn for the horrifying.

It ends up one of the finest examples of homegrown cinematic experimentation, a film that feels alive, blurring real and unreal, and presided over by a man barreling into the unknown with trademark fearlessness. “For me it was absolutely thrilling,” Johansson said back then. “We captured real life on film in a way that nobody’s really seen before.”

‘Under the Skin’ is screening as part of The Independent’s first ever film season at the Institute of Contemporary Arts (ICA) on 24 October. The festival kicks off on 19 October with a pre-event featuring an exclusive screening of ‘Bridget Jones’s Diary’ for Independent Members, including a special reception and on-stage conversation between The Independent’s Editor-in-Chief Geordie Greig and author Helen Fielding.

Membership is open to all, with the top ‘All Access’ tier available for six months available for just £1. See independent.co.uk/membership