Once upon a time, movie moguls were cinema’s biggest mystery. Wreathed in cigar smoke and secrets, the puppet masters who ran the studios were even less knowable than the stars they made and broke.

That is no longer true. Since the fall of Harvey Weinstein, cinema’s big backstage players must be an open book. Press is now necessary – and, for most, highly desirable.

But one enigma remains: Rose Garnett. The head of BBC Films, the broadcaster’s big-screen production arm, she is the great question mark of contemporary cinema. She has never given an in-depth interview and is almost invisible online. Yet those who know her name tend to say it with an evangelist’s whoop – no matter how famous they are.

Garnett minted her Midas touch at Film4, where she oversaw the likes of Room, Three Billboards Outside Ebbing, Missouri and The Favourite (all, incidentally, winners of the best actress Oscar). In February 2017, she was poached by the BBC. Within weeks, she had overhauled team and slate; 70% of the current team are her recruits, and a similar proportion of projects have originated with the new team.

This shakeup is starting to bear fruit. Garnett had three films at Sundance, one of which – Joanna Hogg’s belated breakthrough, The Souvenir – won the grand jury prize. She is also behind the two British films in competition at Cannes: Ken Loach’s Sorry We Missed You – widely reckoned to be better than I, Daniel Blake - and Jessica Hausner’s Little Joe. Coming soon are Jane Campion’s latest, two Sally Rooney adaptations, Renée Zellweger as Judy Garland, and Ammonite, a prodigiously buzzy romance starring Kate Winslet and Saoirse Ronan from Francis Lee, the director of God’s Own Country.

Film4 is understandably anxious. Key talent has migrated with Garnett – and more may follow. “Her record is proven over and over,” says Ruth Wilson, with whom she has a film in development. “She’s synonymous with quality. She’s fundamental to film-making globally.” Even those with whom she’s not currently working clamour to doff their cap. “She’s my kind of woman,” says the director Steve McQueen. “I wouldn’t bother talking if she wasn’t so fantastic.”

I meet Garnett in a small conference room at Broadcasting House called the Queen Vic. It does not smell of lager and there is no visible blood on the carpet. Instead, there are screens, sofas, a platter of satsumas and a 48-year-old woman wearing a T-shirt, a cardie, leggings and trainers: the conspicuously casual outfit of the very powerful.

Being at the Beeb, Garnett says, has made her romantic. She rejects the suggestion that streaming services have spoiled the institution’s pitch: the licence fee is “not very much money in the scheme of things” (Garnett is on £197,500; her department has an annual commissioning budget of £11m) and the BBC “influences all our lives far more than we think”.

Garnett speaks in complete sentences, watertight on her remit: “BBC Films needs to be the best partner it can be: fierce, rigorous, but also fluid and supple and open to surprise and excitement.”

She plays down her own radical changes – it’s the market that has evolved; she’s just playing catchup. The mainstream is now edgier, there’s a keener appetite for films that challenge. Power has shifted from the backers to the talent, so she and her peers at Film4 and the BFI must hustle. Directors such as Chloé Zhao and Cate Shortland can progress straight from minor arthouse hits to superhero blockbusters. “The whole ecosystem is up in the air.”

Voice, not narrative, is in vogue, she thinks, approvingly. “I think we are much better at uncertainty, at complex stories, at flawed characters; that’s just a richer journey.”

Garnett’s great enthusiasm – “Not zeal,” she corrects, “that’s reductive” – is democratising opportunity. “Making a film is incredibly entitled,” she says. “Very few people should get to make a film. It’s expensive and difficult. But our job is to make that entitlement about someone being gifted and passionate and not because of a privilege of birth.”

Garnett has gifts, passion – and privilege. Her parents met at a party in the 60s. Andy Garnett was a charismatic Old Etonian engineer who arrived with his girlfriend; Polly Devlin, a writer for Vogue from County Tyrone. At first sight, Andy’s heart went “Wham bam boom wow” (his words). That night, the girlfriend proposed; Polly asked if he was going to accept. No, he replied, he would marry her instead.

They settled in an Elizabethan manor house in Gloucestershire. Rose was born in 1970, soon followed by Bay (now a stylist) and Daisy (a writer). Andy installed a sprung floor in the barn for ballroom dancing and cultivated a wild flower meadow beyond. He died in 2014. Rose never got into nature or foxtrotting, but she still hears his voice in her head. “I miss him desperately. He was the dude.”

In fact, their bucolic childhood seems to have mostly meant the three girls watched lots of telly: Dynasty, Hi-de-Hi!, Brideshead Revisited and Roseanne. Films, too: The Sound of Music and Ferris Bueller’s Day Off on repeat, plus random classics caught “because you couldn’t be bothered to get off the sofa and didn’t have a remote”.

Garnett flitted between local schools (“I got bored, made trouble”) before settling at St Paul’s Girls’ in London aged 15. There, she knuckled down to work and – says her classmate Rachel Weisz – to read every Mills & Boon, as well as all of Dickens and Eliot. “When she gets into something,” says Weisz, “it’s all or nothing.”

The two became close, went to Cambridge and formed an experimental theatre company (mime, made-up language, interpretative work on a stepladder), with Garnett producing and David Farr directing. “It’s some of the work I am most proud of,” says Weisz. “Tonally, the writing and the shows were absurd: savage and provocative and heartfelt. They allowed Sacha [Hails, the other actor in the company] and myself to play roles rarely if ever made available to girls our age.”

There’s clear lineage, she continues, from that to later collaborations such as Disobedience, The Favourite and upcoming drama Lanny – “projects that move women from the polite periphery to the centre of a story and give them agency and authority”.

In 1989, the three women caught a train to Berlin as the wall fell. “Rose knew it was an important moment and worth the trip,” says Weisz. “She’s very spontaneous and instinctive and it’s exactly like her to say: ‘Let’s do this!’”

Garnett is less forthcoming about her own biography. In fact it is her friend who supplies many dates and details. Garnett seems almost allergic to her own image and squeamish about what she says. The sentences are complete in part because she self-edits before she opens her mouth – and much is off-record. She also has a surprisingly insistent upward inflection; the product, perhaps, of heading a team who are mostly a decade younger, as well as a hesitancy about laying down the law – and laying herself too bare.

After graduating, Garnett went on a secretarial course to learn shorthand and touch-typing (“I wish I had,” says Weisz – “she’s really practical”) before she and Farr took over the reins at the Gate, a small theatre in Notting Hill, west London.

There, they gave early commissions to Sarah Kane and Tracy Letts, making a big impression with a small budget. Garnett met the actor Tom Fisher and they got married. She also met Tessa Ross, later her boss at Film4. “I was very, very taken with her,” says Ross. “She was powerful, warm, clever and inquisitive. Extremely articulate and exciting to be with. All the things you wish for to have by your side. She has always been exceptional and she had not left my brain.”

But Garnett was also hooked on heroin – a functioning addict for four years, she says, until the drugs became full-time. “I was surprised how quickly it can happen and how quickly one can lose oneself.”

She went to rehab, quit drugs and alcohol at 31 and still attends Narcotics Anonymous meetings. “I absolutely subscribe to the total abstinence thing. I think I could probably have a glass of red wine now – but why fuck with it?”

In an industry fuelled by booze, such sobriety might have made Garnett an outlier. Instead, it has lent her edge. She speaks of the pleasure of not being the last one left at the party, of being dependable after years as the opposite.

Yet she is eager to minimise the period’s significance: it is just her version of a bog-standard “shitty 20s”, she tells me twice. “It was a sort of discrete episode that doesn’t particularly feed in or inspire me or keep me going.” Rather, she uses it to illustrate her luck in life: that she got clean young, that she had the funds to cushion the fall.

Nine months after going cold turkey, Garnett gave birth to her first son, George; Frankie followed two years later. “I was feeling quite raw and being able to fall in love and have quite a small universe with my children was just what I needed.” She ended up taking 10 years out to see them through primary school, before Ross lured her to Film4.

If she hadn’t had children so soon, might she have fallen off the wagon? “No. It’s a really crisp feeling, when you decide to get clean.” One she still gets – at home, at work? Absolutely, she grins: it’s her spidey-sense. “You can suddenly go: ‘Oh, we’re going to make this film!’ And you can also be in a room with people who are saying: ‘I can’t wait to make this!’ and know it’s just never going to happen.”

Despite Garnett’s insistence that her dark days were self-contained, and now irrelevant, it is hard not to see their legacy. Endless collaborators flag the unusual clarity and confidence of Garnett’s instincts, the thrill of proximity to that spidey-sense. She admits to a determination not to squander further time – which helps explain the speed of her ascent, despite more than a decade out of the game.

While Garnett is now recovered, the mindset of someone who could do something so dangerous for so long may have found a more productive channel in the relationship with risk she says is central to her role.

“Making a great film is virtually impossible – you should just be incredibly grateful if you happen to be around when it happens,” she says. “There’s nothing you can do to plan it.” Instead, you have to gamble. “We’re jumping off the cliff. It’s really easy to know what you want to make after it’s been made. To go: ‘Yeah, I’ll have a bit of Moonlight.’”

Garnett’s throwaway line about how ditching drugs improved her timekeeping also helps explain the loyalty she inspires; it’s a point of pride for her to no longer be described as flaky. “She’s just so solid,” says the director Andrea Arnold. “Incredibly consistent.” Near the end of the taxing shoot for American Honey, Garnett “appeared one night in some weird hotel in the middle of nowhere in North Dakota. I was just so happy to see her. It was like a blanket. I just felt looked after. But not in a gooey way: Rose is like a rock.”

Arnold also identifies Garnett as an executive in whom it’s unusually easy for film-makers to place faith. “I think she really gets me. But I wouldn’t be surprised if she gets all the film-makers she works with.”

The ones I talk to certainly seem to think so. Garnett appears able to soothe both jittery artists and terrified financiers. She discusses scripts with dignity, says the producer Ed Guiney, but not “a craven respect for the work” – she’s conscious it needs to perform commercially.

That she has no creative-writing ambition helps – her mother’s facility for words made her realise she didn’t share it. Likewise the fact that her aunt was married to Seamus Heaney. He was an exemplary conventional uncle, Garnett reports, who happened to be a Nobel laureate who supplied a special poem for her wedding day.

Big boots to fill. Garnett’s decision not to try to was, she says, vindicated when a script landed on her desk one day that was “thoughtful, perfectly clever, about our lives and boring as hell. And I thought: ‘Oh shit, this is what I would have written.’”

Early exposure to high-end cultural visionaries (as well as Uncle Seamus, her godmother was Peggy Guggenheim – a pal of her father) appears to have left her with immunity to fame. “Celebrity is neither what interests her nor floors her,” says Ross. “She doesn’t have time for fluffing.”

“In an industry where there can be a tendency to exaggerate or flatter or be indirect,” says Weisz, “I think people always know where they stand with Rose. I find her candour refreshing.”

“She’s brutally honest,” says Wilson. “Some of your dreams might be squashed in a meeting, but you know there’s a good reason. She’s got absolutely no bullshit. And it’s really hard in this industry to find people who don’t blow smoke up your arse.”

Like many of the people to whom I speak, Wilson at first rejects the idea that Garnett’s gifts have anything to do with her gender. Yet the more she discusses it, the more she seems to warm to the theory that Garnett’s lack of ego, her desperation not be front-facing or star-seducing are key to the reason she’s central to a business still reeling from the Weinstein revelations.

Garnett met the disgraced mogul only once, when his star was already on the wane. The industry has both changed and remained the same since his public shaming, she says. “People have better manners on them now. They’re more vigilant. If you’re buying a film, does that give you a right to dinner with people in it? Does that mean they have to come on your yacht?

“I’m not necessarily talking about buying sex. But where glamour, money and visibility all meet, there’s going to be a seedy side.”

Garnett is an antidote to all this. Her blend of diplomacy, nurturing and authority is, inescapably, allied to her biology: the key point of difference with those near-mythological beasts who once ruled the studios.

McQueen is more forthright: Garnett’s genius has “everything to do with her gender,” he barks. “I’m happy she’s a woman, trust me. She doesn’t care.” Such honesty is not, he says, something he associates with men. “Plus: if you’re cool, you’re cool. She’s cool. End of.”

• This article was amended on 20 May 2019 to more accurately characterise Rose Garnett’s overhaul of the BBC Films team; she did not replace staff in the team, as an earlier version implied, but recruited new members. This has been corrected.