One fine day a young woman, Keiko, presents herself plausibly to the landlord of a Tokyo apartment as the mother of a studious-looking 12-year-old boy, Akira. Thus established as acceptable tenants (though we wonder about Keiko’s skimpy, armpit-baring singlet, and her childish, high, over-sweet voice), mother and son drag their suitcases up the stairs into the new flat and unzip them. Out pop three smaller children, dishevelled but cheerful.

“May I have everyone’s attention?” says the mother. “I’m going to explain the rules. No loud voices. No screaming. No going outside, not even on to the balcony. And if you don’t do as I say, it’s an enema for you – you’ll eat green peppers.”

She has a flirty, teasing, comic way with them. It’s clear at once, as they sit head to head round the table, guzzling takeaway noodles out of cardboard boxes, that they all adore her – and they must, for how else could she have seduced them into this lifelong conspiracy, this pretence that, except for responsible Akira, they don’t exist? That night, as they settle down on the tatami to sleep, the second child, a girl of ten called Kyoko, whispers to her mother: “The mat smells good. Like leaves, in nature.”

We soon learn that each of the children has a different father, that they are unregistered with any civic authority, and that they have never been to school. Their mother has taught them to read and do simple sums. “If you want to know anything,” she says briskly, on her way out to her mysterious job in the morning, “you can look it up in this” – and whacks down on the kitchen table a paperback encyclopaedia.

At first their imprisoned life seems oddly contented. Sun streams into the cramped apartment. Shigeru, a boy of seven, and Yuki, a girl of four, play peaceably with whatever is to hand. Kyoko sets about her domestic duties, using the washing machine with practised skill and hanging clothes on folding racks. Akira, their conduit to the world, handles the money and goes out for food. Through his serious eyes we see the neighbourhood forbidden to his siblings, its unglamorous convenience stores and pachinko parlours, its jostling schoolkids in uniform whom he silently envies, and whom he and Kyoko long to join. But no, says their mother, because “when you don’t have a daddy you get bullied at school”.

One night the mother turns up tiddly, bearing sushi – “it was a present”. Once the others are asleep she confides in Akira that she is “in love with someone”. “Again?” says the boy. “He’s sweet and serious,” she goes on. “He’s going to marry me. We’ll live in a big house. You’ll go to school.” “Did you tell him about us?” “I’ll tell him – eventually.” The boy lowers his face on to the balcony rail, and for the first time we see the load he is hauling – her flakiness, his weary despair. So perhaps he’s not surprised to wake one morning and find some money on the kitchen table with a note: “Going away for a while. Please look after the others.”

Director Kore-eda Hirokazu has a wonderful eye for ordinariness. He is in love with the tiny, the failed, the almost without meaning. As Akira plods homeward up a flight of stone steps, he passes two little girls playing their recorders with earnest concentration and a complete lack of musical talent. In the convenience store he watches the manager demonstrate to a nervous new checkout girl how to open a small plastic bag; when she fumbles, the manager snatches it and manipulates it with fluid wrists and flying fingers.

Kore-eda’s gift for intimacy and close detail serves him most brilliantly in the restricted world of the apartment. This is the meat of the movie: our entry into the secret lives of the abandoned children. The risks here are sociological indignation, since this is based on a true story, and sentimentality; but gracefully he sidesteps them. Using hardly any dialogue, he speaks volumes with a shot of a child’s socked ankles at a window, a knife slicing an onion, a pencil hesitating over a column of figures, a blunt red crayon being pressed on to a drawing of a skirt, a little crown of gas flowering under a kettle.

His camera sees its surroundings as a child would. He takes items of no significance – sections of furniture, lumps of things on a bare floor – and makes them hum with importance. He understands how a child at play can transform an object into a voluptuous private treasure, soak it in passionate meaning, and use it as a source of comfort. He respects too the weird noises a child emits, in solo reverie: high whines, machine-like throbs, brief expostulations; then fresh tracts of absorbed, uneventful silence.

Nobody Knows is a patient movie, free of exposition, and very quiet. The volume of the city has been turned down. Music might ease one scene into the next, but always softly – a piano, a ukulele, or perhaps a thoughtful little song.

Months pass. The money runs out, the gas, the water. The children go gently feral. The youngest, Yuki, turns five, and to celebrate it Akira smuggles her down into the street at night in a special dress. He walks beside her in the dark, looking down at her happiness with the terrible wisdom of the older child saddled with too much responsibility.

“I keep feeling,” said the 13-year-old girl who was watching the movie with me, “that something awful’s about to happen.”

“Their mother’s dumped them,” I said. “What could be more awful than that?”

But she was right, of course; with a tender obliqueness, not sparing us, Kore-eda renders the unbearable, and draws the story to its troubling resolution.