About four years ago, Paul Thomas Anderson got sick. “Just a bug. Inexplicable. It wasn’t food poisoning. It was just one of those things that takes you over.” Tended to by his wife, Maya Rudolph – she of Bridesmaids’ most memorable gastrointestinal moment – Anderson hatched a plan: a movie about the tenderness of the invalid and the power of the nurse. About whether the odd bout of illness might sometimes be healthy.

Phantom Thread – exquisitely styled, emotionally raw, macho saturated – looks like classic Anderson. Daniel Day-Lewis, who won an Oscar for the director’s There Will Be Blood, is back as another ravenously charismatic obsessive, Reynolds Woodcock, a brilliant, brattish couture designer in postwar London. But strip away the cravat and you find a pussy bow. Phantom Thread is a subversion – a hymn to women’s upper hands and stronger stomachs. For Reynolds is upstaged by his sister, Cyril (Lesley Manville, on super-wither), and turned subservient to new muse, Alma (Vicky Krieps). A fumbling, blushing immigrant waitress, Alma is whisked off to Reynolds’s London fashion house to act as a live-in muse, and initially appears no match for the suave genius 30 years her senior. Yet Reynolds underestimates her at his peril. As do we. Watch the movie a second time and all her entreaties – “Whatever you do, do it carefully”; “Maybe I’m looking for trouble” – sound like threats.

The film is a perfectly timed portrait of patriarchal crumble. Accidental, of course. “It’s funny,” says Anderson. “They land when they land. You really can’t account for what the world’s gonna be. Back when we started this story I didn’t think Trump would be president; I didn’t know where Harvey Weinstein’s life was headed. And here we are.”

Claims for Reynolds as an archetype of toxic masculinity are, he thinks, “a bit thin. He’s just your standard-issue self-absorbed, spoiled-baby fashion designer in Fitzrovia in 1955. He’s not ripping his shirt off and doing jello shots.”

Anderson’s 2011 film, The Master, was produced by Weinstein. At the time, Anderson spoke of his love for a man who had taught him so much. Today, he wrinkles his nose at the name. Talking about him would be “yucky”, Trump likewise. “Do we have to?” But he can’t help himself. The president, he thinks, would “freak out” even Anderson’s most extreme characters, The Master’s Lancaster Dodd and There Will Be Blood’s Daniel Plainview. His shadow haunts Phantom Thread. During preproduction in London, Anderson flew back to Los Angeles to vote, gleefully anticipating a Clinton victory.

“Because of Brexit, everybody was like: ‘It’s going to fucking happen to you, man. Open your eyes.’ And, of course, we were like: ‘Naaah.’ Getting on a flight back to England the day after the election was horrifying. Really, really not a good feeling. People said: ‘You’re picking the right time to leave the country,’ and it was like: ‘No, it’s the reverse, I don’t wanna leave here right now.’”

The first day of the shoot fell on Trump’s inauguration. “It was a rocky start. The concentration the first couple of days was not there.” The results gleam, but the process sounds rough. Krieps has spoken of on-set claustrophobia; Day-Lewis called it a “nightmare” that left him with such a profound sense of sadness that he quit acting.

Anderson understands. “Things are always melancholy at the finish line of a film. I think mine was short-lived because my friend and mentor Jonathan Demme died on the last day of our shoot. I was on a plane to his funeral the next day and thrown into the icy-cold waters of mortality and sadness of a different kind.”

That last quote he emails over a few weeks after we meet. It’s the sort of writerly line you suspect he would never say out loud. Anderson treads lightly and speaks briefly. Online and in the flesh, he’s as straightforward as his films are grandiose; as accommodating as his films are ambitious.

Touted as the successor to Demme, as well as, variously, Altman, Scorsese, Coppola, Truffaut and – since Phantom Thread – Hitchcock, he still behaves like a first-timer who is eager to please. His Reddit threads and Twitter Q&As are relaxed and irreverent. At an awards ceremony in New York this month, he asked Manville to read out his phone number from the podium so Tiffany Haddish – the Girls Trip breakout star – could give him a call. He’s polite and solicitous, even when his laptop all but explodes in his rucksack (“Ooh, that’s not a good smell …”).

At 47, he dresses like an upmarket jumble sale on legs: old T-shirt from Rag & Bone, mossy Oliver Spencer felt trousers (“not itchy at all”), two-tone brogues with snazzy string detailing. “Somewhere between snazzy and Scandinavian. They’re a bit fucking Danish, but there we are.”

What we wear, he says, is chosen to “make us feel we can get through the day. Right now, the thing I’m projecting is comfort. I live in a place where I can be in a T-shirt and shorts 90% of the time. To think I have to put a turtleneck on and a coat just to get across the street is still a chore to me.”

Anderson was born surrounded by sun and screens in Studio City, California, the seventh of nine children, raised Catholic by a voice-actor father he adored and a mother he didn’t so much. He told people he was to be a film-maker before he got his first camera, aged eight. He has never made a dud. The gambling neo-noir Hard Eight (1996) was a virtuoso debut; porn extravaganza Boogie Nights (1997) got the public on side as well as the critics, ditto ecstatic ensemble piece Magnolia (1999). Punch-Drunk Love (2002), a fruitloop romcom with Adam Sandler and Emily Watson – and the movie Phantom Thread most resembles – proved more divisive, as did 2014’s baggy Thomas Pynchon adaptation Inherent Vice. But There Will Be Blood (2007) and The Master stand tall as two of the century’s bona fide masterpieces.

Yet unlike most of the men who drive his movies, Anderson does not seem to be defined by his work. He and Rudolph have been together for 17 years and have four children whom, he says, he doesn’t let out of his sight. His longest answer of the interview is about what he gives them for breakfast (in brief: miso soup, pancakes, eggs, bagels, Cheerios).

The domestic is vital, off-screen and on. “I was always of the philosophy that you can tell a lot about a character through what they order for breakfast,” he grins. Reynolds’ epic brekkie order near the start of the film – “welsh rarebit with a poached egg, bacon, scones, butter, cream, jam, a pot of lapsang souchong and some sausages” – should, he thinks, have been a red flag for Alma, who is working as a waitress when they first meet. Likewise, that Reynolds speaks so highly and frequently of his late mother. “Three times on the first date? Ding, ding, ding!

“What happens when your mother hasn’t let your feet touch the ground, or is convinced the sun shines only for you? When you have this halo that means as long as you’re creating, you’re allowed to behave as inappropriately as you want to. There’s nothing worse than kids acting like the worst kind of adults and adults acting like the worst kind of kids. That’s not a good look for anybody.”

Yet isn’t it one that is in vogue?

“You do see a lot of that. But I think we can do better.”

He talks about how hard he finds it to fathom artists, such as Picasso, who are so self-consumed they cast aside children in service of their work. And then, with deference and bewilderment, about Versace, Gucci and McQueen, and their unusual familial closeness.

Anderson’s brush with fashion in Phantom Thread does not seem to have left him with a taste for togs. Perhaps it’s a chilly business for someone most at home in flip-flops. Certainly, he says, getting measurements taken is “potentially soul-crushing. It’s such an intimate process. You’re sort of wondering: 32 – is that good? Sixty-four? Sixty-four what? Where am I on the scale?”

Maybe there’s something morbid about fetishising frocks? He pauses diplomatically. “Looking at a beautiful dress when it’s lying on a slab in the V&A, you see the construction and the history and the hands that have made it. But unless it’s on someone, it’s sort of like roadkill. Just sort of lumpy.”

One of Phantom Thread’s most revealing – and amusing – scenes comes at the end of Reynolds’ and Alma’s first date. Rather than undressing her, he critiques her physique as she models a new gown. “You have no breasts,” he comments. She apologises. “No, no,” he replies. “You’re perfect. It’s my job to give you some. If I choose to.” Anderson half-cackles, half-shivers, quoting it back. “It’s Frankenstein’s monster to some extent; this creation they want to bring to life. If the breasts are too large it may distract from their creation …”

Over by the window, where it has been cooling off, Anderson’s laptop bleats: another victim of a mysterious bug, its fate in the hands of others. It does seem sick. And whatever document is frozen on screen looks scripty – and unsaved.

Anderson goes over, gently presses a couple of buttons and coos soothingly. “OK, OK, I think we’ll be alright,” he murmurs. The saviour of serious American cinema, patient as a nurse. And cheerful as one, too.

• Phantom Thread is released in the UK on 2 February