David Mackenzie could be on the verge of big things with his new film, Hell or High Water. It has already received sobbing notices and impressive results at the US box office. It has been hailed as the saviour of modern indie cinema, and as a brilliant throwback to the glory years of the Hollywood new wave.

With a big-name cast – Chris Pine and Ben Foster play bankrobbing brothers, carving a trail of havoc through west Texas, Jeff Bridges the curmudgeonly lawman on the case – and a pedigree scriptwriter (Sicario’s Taylor Sheridan), Hell or High Water has unexpectedly emerged as a prime example of a kind of muscular, full-blooded American cinema that was largely thought extinct. And, even more unexpectedly, Mackenzie has seen a sudden leap in his own profile: not quite a Hollywood A-lister, perhaps, but certainly a step-up from the peripatetic auteur status he has hitherto accrued.

Mackenzie’s reputation as the most self-effacing of film-makers appears to be borne out by his quiet, almost tentative, speaking voice (as well as the impressive, face-concealing beard he is currently sporting). Hell or High Water, he says, was a “love at first sight experience”, when he was sent Sheridan’s script as a spec project: “I very rarely read a script that I don’t feel I want to change a lot.” Mackenzie acknowledges that the Hollywood new wave comparisons are apt – “It had the freewheeling vibe to it that I love in 70s movies” – but suggests that depression-era outlaw stories (of which the new wavers made plenty, such as Bonnie and Clyde, Dillinger and Thieves Like Us) was as much of an influence on Hell or High Water’s social comment. “It’s a reclamation of some kind against forces that are bigger than people. I wanted that Pretty Boy Floyd atmosphere.” He says the name given to Pine and Foster’s characters – Howard – is “a sly reference to Jesse James’s alias”.

David Mackenzie at the Cannes film festival in May this year, for the showing of Hell or High Water. Photograph: Pascal Le Segretain/Getty Images

James, of course, belongs to an earlier era of American outlawry, but the point is well-made; it is the sense of economic hardship, bred in the bone for generations, that underpins the brothers’ criminality, and is exactly what US audiences – in the era of The Big Short, the Trans-Pacific Partnership and Trumponomics – wants to hear. “I’m an outsider; I’m not involved in American politics, but these themes are there to be picked up on. I can shine a light on them, I can touch on them, but I am not in a position to ram them home. That’s not my sensibility anyway.”

But exactly what is Mackenzie’s sensibility? Though a staple of the festival circuit, and a pillar of the Scottish film industry, he is remarkably hard to pin down, as a director at least. Hell or High Water is Mackenzie’s ninth feature, released 14 years after his first, The Last Great Wilderness. Young Adam, the Alexander Trocchi adaptation he released in 2003, remains probably his most admired film; the Jack O’Connell prison flick Starred Up – until Hell or High Water came along – the closest he has come to a popular success. He has a proper body of work to his name, but if it is distinguished by anything, it is by its pinballing, switchback nature: a determined effort not to go over old ground, to the extent that the usual evidence of directorial signature is almost entirely absent.

“I think there are connections between them,” Mackenzie says, frowning. “But it’s true, it’s quite hard to pin down what they are. I’m not doing it wilfully; in the early days, I was just trying to do something original each time. Signature film-making seems rather dull to me; it’s about finding something you can do something with, and running with the ball.”

Jack O’Connell in Mackenzie’s 2013 film Starred Up. Photograph: Allstar/Film4

Mackenzie talks about “tuning into” or “assimilating” into the world of each film – whether it is the Marfa, Texas, of Hell or High Water, or the grimy sludge of T in the Park for his guerrilla-shot music festival romance You Instead. “A lot of cinema is about the game of authenticity – do you feel it’s real?”

“As a director, when you embrace a project, you try to understand as much as you can about its world, and you do that by embracing and engaging with people who are in that world. Then it’s down to your best instincts, which is what most directing is about anyway.” Describing himself as a “navy brat”, he mentions an itinerant childhood as a possible source for this habit (he is the son of Rear-Admiral John Mackenzie, a senior officer in the Royal Navy). Directing, he says, “is all about an alchemy, a dance”; on set, he says, he is “trying to steer towards what’s needed”. “If you ever have to do any hard steering, it feels less than ideal. It’s a gentle dance. I don’t know if I explained that very well.”

Despite You Instead attracting some unkind reviews, Mackenzie credits the film with loosening him up as a director: choosing to shoot an entire feature in five days in “the most uncontrollable environment you could possibly make a film in” was “an amazingly liberating experience”. “We had to roll with the blows and the circumstances at any given moment. We had to evolve our technique, shooting with longer lenses so people wouldn’t notice the camera.” Now, he says, he doesn’t “really give a fuck about originality”, and is less uncomfortable with genre films. It is no coincidence, surely, that his recent critical and commercial surge has been due to taking on those very genre films – Starred Up, Hell or High Water – that he spent so long avoiding.

Ewan McGregor and Emily Mortimer in Young Adam, 2003. Photograph: Allstar/Hanway Films

Thinking back, he says that in the late 90s and early noughties, when he was making award-winning short films and developing his first features, his main inspiration was Danish cinema, and the Dogme 95 movement in particular. “It punched above its weight for a small country and made some incredible stuff. It was very hard not to admire it from the outside, and think that it was possible to do something like that in Scotland.”

It didn’t work out that way, says Mackenzie, but Sigma Films, the company he founded with his production partner Gillian Berrie, has been very thick with Lars von Trier’s Zentropa over the years: joint credits include Red Road and Wilbur Wants to Kill Himself (from the “Scottish Dogme” scheme Advance Party) and von Trier’s Dogville. Zentropa also helped Mackenzie’s debut, The Last Great Wilderness, into production; it looks very Dogme-ish now, with its frenetically mobile low-tech video camera.

His attachment to Danish cinema may also have led to his career low point; he readily admits to finding his ambitious end-of-the-world fable Perfect Sense – from a script by Danish writer Kim Fupz Aakeson, and backed again by Zentropa – a difficult and, at times, disorientating experience. He says he found it “emotionally hard”, and that he “tried really hard, but I was going home every night and asking whether we really knew what the idea was supposed to be. I’ve never felt less comfortable as a director.”

Jeff Bridges as the lawman, with Gil Birmingham as his sidekick, in Hell or High Water. Photograph: Allstar/FILM 44

Perfect Sense does, however, fit into the narrative of reaction and about-turn that is how Mackenzie describes his film-making progress. The barebones simplicity of You Instead was, he says, a reaction to Perfect Sense’s overwrought, Melancholia-style imaginings, while Perfect Sense was itself a high-minded response to his first, not entirely comfortable, American production: the Ashton Kutcher sex comedy Spread. Released in 2008, Spread is by some way Mackenzie’s most unlikely film; and one that, despite its confidence and fluency, appeared to sour Mackenzie against a planned full-time shift to LA. He doesn’t go into detail, but admits: “There was a little bit of negativity between myself and the producers, and it left a nasty taste in my mouth. I don’t really want to go there, as it feels a long time ago and the final film is my vision – but gentlemanly behaviour wasn’t going on.” Instead, he went back to Glasgow and got on with Perfect Sense.

Hell or High Water is his first venture in the US since Spread, and it seems that the credibility he derived from Starred Up put him back on the radar of US producers. Starred Up wasn’t a commercial success in the US, he says, but – as he rather sheepishly points out – despite “not being particularly macho in the way I live my life, somehow or other it allowed Americans to regard me as someone able to deal with macho subjects”. Having extracted what could well be a career-changing performance from Pine, Mackenzie would appear to be set fair for a proper tilt at Hollywood.

Only then does his careful, diplomatic manner break down, after I suggest that Marvel – with its current penchant for indie directors – might be considering putting in a call. “I can’t fucking bear superheroes, so I won’t be doing one of those.” It is the nearest he gets to actual asperity; fortunately, Hollywood is a big place, and Marvel is not the only game in town. “I look forward to the day when the general public get tired of these things – I’ve been tired of them for a long time.”