When Vicky Krieps falls in love with Daniel Day-Lewis on screen, it is a moment that seems unrehearsed in its intensity – and that’s because it was. Day-Lewis insisted that Krieps, a barely known actor from Luxembourg, meet him for the first time in character in Paul Thomas Anderson’s breathtaking new film Phantom Thread. Preparing his role as Reynolds Woodcock, a London couturier, Day-Lewis – with his habitual method-actor zeal – learned to think like Balenciaga, sewed 100 buttonholes and kept Krieps at bay. When Krieps’s Alma walks into the breakfast room of a Yorkshire hotel with sea views, she looks as shy as a Raphael Madonna, but in a waitress’s uniform (the film is set in the 50s). When she asks, in her lilting German accent: “What would you like to order?” Woodcock starts to reel off almost everything on the menu. And Krieps blushes – for Alma and herself. For the audience, there is never any doubt that Woodcock’s appetite – and this is a film about appetite – is not for what is on the menu but for this young woman who will become his muse. Last summer, Day-Lewis announced that the film would be his swansong. For Krieps, it is the most extraordinary beginning.

The New York Times critic AO Scott has described Krieps as, in every way, a match for Day-Lewis, an actor at once “canny and unintimidated”. She is a sensation: she brings to the role beauty, vulnerability and a stubborn – potentially defiant – serenity. The film is being hailed as Thomas Anderson’s best (and Magnolia and There Will Be Blood are hardly easy acts to follow). It is at once disturbing and enigmatic, but not without comedy.

As Krieps sits down beside me for coffee in a Soho hotel, I cannot resist asking whether she has ever been a waitress in real life. She exudes charm but does not look as if she would necessarily be a safe pair of hands with a tray. Her unmade-up face is open, sensitive and intelligent. Her clothes are casual but dashing: she is wearing a black fur bolero and her salmon pink cashmere cuffs double as mittens. “I’ve been a waitress for events, but a lady at the Victoria hotel in Yorkshire showed me how to do it properly.” And she starts to demonstrate various ways to serve “from the right, not from the left”. Bending from side to side, supple as a willow, she makes me laugh and protests that the staff at the Victoria – in Robin Hood’s Bay – told her she was a “born waitress”, adding that should acting let her down, she would have no difficulty getting a job.

There was no plan. We just did it… I felt as if I were on a boat so far from land, I didn’t know how I would get back.

Thomas Anderson happened upon Krieps by chance. He saw her play another sort of servant in The Chambermaid Lynn (a 2014 German black comedy for which she won the German film critics’ award for best actress). The film was only available on iTunes for a week – Anderson might easily have missed her. And Krieps (who speaks German, French and English) was so far from expecting a big break that she neglected to read the crucial email from her agent properly. She somehow got it into her head that she was auditioning for a student director from London. It was only after she had sent in the audition piece, filmed on a mobile, that she learned from her agent (who was by this stage incredulous at her breeziness) that Paul Thomas Anderson was the director and that, were she to be cast, Daniel Day-Lewis, record-breaking winner of three best actor Oscars, would be her other half.

I tell her that what I found most striking about that first meeting between them in the hotel breakfast room was the look of knowledge on Alma’s and Reynolds’s faces. They had never met, yet it is as if, on some level, they already knew one another. Perhaps this is what sexual attraction is? That look, she replies, was, “anticipation”. Love was never talked about, she says, but always there: “a ghost in the room”. I guess that Day-Lewis’s intensity must be contagious? “It is – he asks you to be very aware and awake. Their love, like all real love affairs, begins as recognition. They see each other.” Not having rehearsed made her “more nervous than I might otherwise have been” but it was a “powerful experience to discover someone as you are working – I think this is what he [Day-Lewis] intended”.

Krieps confesses that there was a day before filming when there was a danger of them meeting but swears she spent it “looking at my feet. I thought: if that is the rule of the game, I’ll play it. I spent a whole day staring into greenery to avoid him.” She also took herself off on long walks by the sea, calming herself that way. She knew that once she became Alma, she would have to meet Reynolds’s gaze incessantly, and the man who started out charming would turn out to be overbearing, testy and needle-sharp. Day-Lewis plays him with a compelling inwardness. His eyes are hypnotic (his eyebrows incredible). Would she say their relationship devolved into a power struggle as Reynolds became less flirtatious, more despotic?

“I see it not as a duel but as a duet – a dance.” She goes on: “The power levels are different in Alma and Reynolds. Paul left this very open. Many relationships can become difficult and it can be hard to find a way back. Alma finds a dangerous way [it would be a spoiler to elaborate]. Sometimes, if you look at older couples who have been together for years, they have the strangest ways of staying together – they play games, often sexual.” To be Alma, she suggests, was to surrender to a riddle: “She is like an equation you can’t solve – a poem.” Krieps steeped herself in Emily Dickinson’s poetry as a gloss on the character, a way of reaching “beyond what we know”.

The closest she comes to explaining Alma is in terms of the second world war and its after-effects: “Alma has seen people die. She has seen what it means to lose your home and country. She comes from cold, windy Germany and is transported into a warm world in London, wrapped in silk and light. People who live through the war cannot think about themselves. They cannot ask: ‘Am I weak?’ ‘Am I strong?’ They just have to get up and be brave.” And being brave – although she would be the last person to boast – comes naturally to Krieps.

“When I was 26,” she volunteers (she is 34), “I got pregnant. I decided to have the baby because I accept everything in life as an adventure. I accept life. I couldn’t see why you would not accept it. I was naive – I didn’t realise what it meant…” and she laughs and leans sideways on the hotel banquette, completing her sentence with a pretend swoon. She has a delicious sense of comedy – she sends herself up in a way only someone who takes themselves seriously would dare to do. “When I got pregnant, I knew I wasn’t anywhere in my career, that I had not arrived. I was still on my adventure and so I said to the child in my belly: ‘I am so happy for you to come but you should know I’m still on my way and you’ll have to come with me and be in my rucksack.’” Krieps’s partner is German actor Jonas Laux. Her daughter, Elisa, is seven.

I find it heartwarming that, without prompting, she smuggles her daughter into our conversation so soon, almost before saying anything else. And I reflect that Krieps’s self-confessed tendency to take whatever life brings is a quality that informs her Alma. “Like Alma, I am strong-willed, opinionated, unafraid to speak out. I love nature. I have a sense of playfulness. I understand Alma’s longing to be in a different place. I come from Luxembourg, a country so small you always feel the world is elsewhere and want to get on the next train out to see what’s happening.” But in other ways, she and Alma are different: “I lack her patience and trust in love. Alma is softer than me.” Krieps once commented in an interview that she believed in “chaos” – a startling assertion. Today she talks about the power of sehnsucht in her life and Alma’s: “It is a wonderful German word, I don’t think there’s an English equivalent – the longing for something you once had combined with a yearning for something as yet unknown.”

The film is a love affair with texture, its camerawork a form of tailoring. It is made with a perfectionist’s eye but it is claustrophobic, uncanny, bizarre – it will make you feel at once dazzled, hemmed in (pun unintentional) and rapt.

Lesley Manville, seated left, and Vicky Krieps in a scene from Phantom Thread. Photograph: Laurie Sparham/AP

Krieps loved her fleeting insight into haute couture, appreciating, in particular, the sense that “time is stitched into each dress”. She emerges as a sensualist – and although she professes never to have been detained by fashion, she prizes beautiful needlework, describing in detail a still-cherished frock that once belonged to her grandmother and is now worn by her daughter: “Greek in appearance, embroidered in blue and silvery thread, cut off at the shoulders.”

Thomas Anderson recruited meticulous seamstresses (not all actors) to be in the film and Krieps enjoyed going to an atelier at Central Saint Martins college in London to watch them work: “Two of them were from the V&A. It was great for us – I really wanted to learn as we were shooting.” But what frightened her, strange though this might sound, was having to model the clothes: “I got so scared, I couldn’t sleep – I was afraid of tripping over my dress, falling, ruining the whole thing. I grew up running about in trousers. And so to act in the modelling scene, I studied and imitated Pathé films of models from the 50s. The scene is silent but has such layers, with all these dresses coming alive.”

In a recent interview in W magazine, Day-Lewis, now 60, confessed that making Phantom Thread had “overwhelmed” him with a “sense of sadness”. It had, he said, been fun discussing the movie in advance and he and Thomas Anderson had laughed a great deal – until the laughter stopped. “That took us by surprise: we didn’t realise what we had given birth to. It was hard to live with. And still is.” He has not seen and does not plan to see the film – a decision connected to making the divorce from his career complete. Krieps’s own line on Day-Lewis’s retirement from acting (about which she has been repeatedly asked) is understandably circumspect: she respects his decision but acknowledges that she would celebrate with the rest of us were he to change his mind.

Much of the film is shot in a Georgian house in Fitzroy Square, in central London. Something about the filming there made Day-Lewis feel he could not go on – and at the same time, that he could never stop. What actually went on?

Krieps begins by detaching herself from any sense that the filming was claustrophobic, saying that she and Lesley Manville (who plays Reynolds’s sister Cyril with waspish poise) appreciated the space, that the house seemed luxuriously large. But she then lets slip that for her, too, the atmosphere was all-consuming. It was more like living than filming: “There was no plan. We just did it. We trusted in something, I don’t even know what. Making the film felt endless – Paul had the same impression. I felt as if I were on a boat so far from land, I didn’t know how I would get back.” And, outside the house, London appeared weird, “with people from 2017 walking around – I got frightened, which I wasn’t expecting. It surprised me.”

This imaginative suggestibility can in part be explained by Krieps’s fairytale childhood. “I grew up in a house in Hesperange, Luxembourg that stood on a hill, next to a castle,” she remembers. “The house looked down on to a valley and was built out of the ruins of the old castle walls. As a child, I once hid all my mother’s jewellery in the ruins for my brother and sister to find. It was forbidden to go inside the castle but we went in anyway. Unfortunately, they couldn’t find all of the jewellery [she laughs as if still slightly shocked by the memory] but it wasn’t expensive – my mother was a hippy – so she wasn’t too mad at us.” As a teenager, she remembers daydreaming with her friend Eileen (now a director), who lived next door. “We drank tea, we listened to Suzanne Vega and shared picnics in my garden.”

In Krieps’s life, reverie has always been offset by rebellion. On leaving school, she caused a “little scandal” with a parting speech in which she condemned Luxembourg’s education system. She declared: “Thank you for giving me a diploma. You have given me proof that I know how to learn off by heart, that I know how to copy and how to shut my mouth.” And then, not long after this outburst and the subsequent uproar, she left for South Africa, travelling on her own, and worked in a township before going on to Mozambique. This time in her life was pivotal: “It is important to have a distance. You need to get away from home to see where you come from. If I’d not gone to Africa, I’d never have had the confidence to say I wanted to become an actress.” The “extraordinary beauty” of Mozambique and its beaches, the sense of life as “miraculous and brief” moved her, made the stakes seem higher. She is a bit of a pantheist – the “connection with nature” was crucial. But there is nothing soppy about the way she tells it. She is sure of what it is to be a romantic. She felt the necessity of “doing what your heart is telling you”. And her heart was telling her to act.

The problem was that, in Luxembourg, deciding to be an actress is like announcing an intention to “go to the moon”. It was not expected. Her grandfather, Robert Krieps, a wartime member of the resistance, was a “big politician who abolished the death penalty. He could not shut his mouth and many people did not like that. I once felt that I’d have to follow him – become a lawyer or go into social work.” Her mother had studied art but never finished her degree. “She was, above all, a mother.” Her father studied politics and history and was a manager of a film distribution company, but she emphasises that this was incidental – he was more interested in management than film.

‘We would often film a scene just once or twice’: Daniel Day-Lewis and Vicky Krieps in Phantom Thread. Photograph: Alamy

Defying family with her newfound confidence, Krieps got out of Luxembourg to study drama in Zurich’s University of the Arts. And, in her last term there, she staged another mini-rebellion. She decided to write and direct her own play instead of performing the required monologue. “I was 25 and my play Kopf Ab – ‘Head Off’ – was, I suddenly realised, a version of Faust.” Finding herself with only two weeks of rehearsal remaining and short of a Mephisto, she rang her mother – who is not an actor – and asked her to step in. “I told my mother to go from right to left, eat a clementine and drop the peel slowly. People would come and say the actress who played Mephisto was ‘incredible – especially that look she gives into the afterlife’. Actually, that was my mother checking on me doing lighting and sound upstairs and wondering if she was doing the right thing.”

The play went down so well that Krieps was invited to write and direct for Theater an der Parkaue in Berlin. She has lived in the city ever since. It was in Berlin that she was spotted by casting director Simone Bär (Inglourious Basterds), who “put me up for supporting roles in Joe Wright’s Hanna [2011] and, in the same year, Roland Emmerich’s Anonymous”.Today, while she acknowledges the difference between independent films and a movie like Phantom Thread, she believes “one form should never be elevated above another. All work is equal – if it is good work”. She will, according to IMDb, be in Julien Temple’s film about Marvin Gaye, Sexual Healing – but at the moment does not know (or is not ready to reveal) what she will do next: ‘I am not particularly interested in changing my career, I like European movies.’ It is delightful to see how unswayed she is by celebrity: she is a hype-free zone. And she seems refreshingly unfocused on the idea of becoming a star herself. But there is no mistaking her enthusiasm for Paul Thomas Anderson’s non-interventionist faith in her. “I trusted Paul. If he did not say anything, it was good. We would often film a scene just once or twice. I didn’t get much direction – it was wonderful.”

One word in the film stands out because Krieps’s Alma makes it her own. It is “yes”, and each time she says it, she gives it a new character – you have the sense of risk, of not knowing where acquiescence will lead. “As I said the first ‘yes’, it felt like something was lifting off the ground,” she remembers. And would she agree acquiescence of this sort is rare nowadays? “It is rare because we have lost our openness. We don’t say ‘yes’. We think: ‘Do I look OK? What is she going to write? What will people read? God – maybe people won’t like me.’”

I cannot imagine anyone not liking Vicky Krieps. And I just want to ask: was it easy to locate in that small word an endless sense of possibility? “Yes,” she says.

Phantom Thread is out 2 February in the UK, and is out now in the US