No prizes for guessing the hottest art ticket in London town this season, so far: the Hockney landscapes. But now, Lucian Freud Portraits over at the National Portrait Gallery puts in very strong competition. It’s an unmissable show: iconic works everywhere plus rarely-seen portraits, selected in close collaboration with the artist for a show that was intended as a celebration of “Britain’s greatest living realist painter” but became a retrospective following his death in July last year. He was 88.

Lucian Freud’s subject is well-known. He does nudes. More accurately, he does people. They sit or sprawl or stand, they lie foetus-like, or legs akimbo, with dog or plant or object acting like some medieval attribute, sometimes looking out, sometimes eyes downcast, and oftentimes asleep (he painted in shifts, day- and night-time, sitters never meeting). And not all were nude. Clothes were painted as carefully as the flesh he famously exposed in uncompromising colour and contour.

What an arresting, eclectic, puzzling group of people he gives us. Not all are named. They are ‘the people in my life’, he said: lovers, friends, family. He did not try to flatter. Self portraits come with equally hard-nosed scrutiny. These are psychological portraits, made with merciless powers of observation, perhaps befitting the grandson of Sigmund Freud. Freud had no time for such things, but it can’t be denied the two followed similar paths, having intense one-on-one dealings with a subject, analysing by speech or paint.

The earliest portrait is Cedric Morris, his tutor at East Anglia, by Freud aged 18. Like others in the opening room it typifies his early style: thinly painted using fine brushes, tight, almost photographic in detail. Several show Kitty Garman, Freud’s wide-eyed first wife, Girl with a White Dog (1950-1), for instance. Go in close and you see the stray hairs on Kitty’s head, the dog’s whiskers, the soft tissue of its pricked-up ears, and the liquid reflections in all four eyes. His style changes later. He paints standing up, uses coarser brushes and lashings of paint, resulting in more vigorous work. By 1975 and the portrait of Frank Auerbach, focused firmly on his domed forehead, he’s using Cremnitz white, a stiff dry pigment to help him replicate flesh textures. Auerbach said: “The subject is raw, not cooked to be more digestible as art . . .”

Raw they are, often disquieting, carrying a mood of alienation. Yet not all: works like Benefits Supervisor Sleeping are magnificently affectionate.

Whatever the emotional charge, Freud’s portraits are intriguing. These are real people, so real you want to account for them. Why so often do his subjects look uneasy? Why that hard stare (like Freud’s own)? Why looking down or away? Were they told to do this? Or lulled into slumber by the eternity of the sittings? He was notoriously demanding of his sitters. Until May 27. For Freud’s portrait of The Queen we have to wait till May and the National Portrait Gallery’s exhibition The Queen: Art and Image.