A stunning image opens this show: of a small woman balancing on a towering stool to paint a substantial canvas on the wall. Look twice and you see that she is working on a picture of herself, larger than life and clearly made without any use of a mirror. Her shadow on the rear wall is larger still, and so gracefully painted by the South African artist Lisa Brice as to amount to a third portrait of this woman, namely the Dutch painter Charley Toorop (1891-1955), whose art has only recently received its due.

Brice’s triple portrait of Toorop, painted in hazy monotones, literally raises her up, enlarging upon her gifts, her self-knowledge and struggle. It is a highly intelligent hymn of praise, a spellbinding commemoration.

It is also the ideal herald for what follows, which is nothing less than a show of enormous and lifelong devotion to painting by 31 contemporary artists, many born elsewhere but who all now live in Britain. The oldest is in her 80s, the youngest under 30. There are painters of renown – Rose Wylie, Peter Doig, Lubaina Himid – and newcomers lately out of art school. Painters known abroad more than here, and painters whose star ought to have risen long ago, such as the Grenada-born Denzil Forrester, whose visions of the dub and reggae scene in south London reprise futurism in chemical colours.

Since each artist is represented by several works, beautifully displayed with plenty of radiant thinking space in architectural enclaves, there is the feeling of seeing many small shows. Yet there is a constant and unifying energy to the whole experience – rich, absorbing, eventful, and as connected to the life of our times as anything in contemporary fiction.

The Iraqi artist Mohammed Sami paints a door ajar in the corner of a room, its shadow falling on a picture of an arm upraised, instantly recalling Saddam Hussein. In the foreground, a spider plant throws its shadow on the door, in turn conjuring a monstrous black widow slipping into the home. A double horror, and made this year, the painting’s title is Infection.

The Zimbabwean artist Kudzanai-Violet Hwami, a recent graduate of the Ruskin School of Art, assembles four panels in a grid – a still life of banana plants, the rear view of a man walking away, two lovers embracing, a painted facsimile of a family photograph, possibly featuring the artist. Perhaps they are connected, related; certainly, a story seems to beckon. Whatever it is, the connections are both private and entirely public, like the grid of scrolling images on an Instagram account.

The German artist Sophie von Hellermann paints dreams, figments, tropes. A lone figure marooned beneath scarlet skies on a desert island. Some strange memory of a woman running through fields as a plane hunts her down. A girl in a long dark dress, arms outflung in horror as she overturns a chair, with the title Hysteria, and painted under lockdown. The wispy paint arrives on the canvas like a phantasm.

Narrative prevails. An egg rolls perilously close to the edge of a table. A girl’s palm is read. A woman opens a door, breathing blue smoke at the viewer. On Anywhere Street He Slips Unnoticed… is both the title and the story of Caroline Coon’s sardonic painting of a man furtively visiting a London brothel.

Matthew Krishanu’s small paintings of two little boys evolve into a poised but disturbing sequence of freeze-frames. Here they are on the prow of a boat in high water, or suspended on a log above rushing torrents. Now they are way up in the mountains, reading books in deckchairs outside their tent. Why – how – are they always out there alone in the world? Krishanu’s paintings are a meticulous balance of tension and meditation.

Although there is mercifully no curatorial agenda in Mixing It Up: Painting Today – other than the belief of the Hayward Gallery’s director, Ralph Rugoff, that the UK currently has one of the world’s great painting scenes – there are definitive groupings in the presentation. An upstairs room is concerned with illusion, specifically the paradox of depicting the 3D world in two dimensions, notably in the optical trickery of the German artist Daniel Sinsel’s painted reliefs, which send the eye in and out of space, and sometimes into deep black holes. And in the Chinese painter Vivien Zhang’s scintillating collages of digital pixellations, video glitches and old-fashioned scrolling ribbons: the millisecond speed of the computer age rendered in slowest paint.

One space is devoted entirely to abstract painting, and most particularly the huge dragged and mauled canvases of the Colombian-born Oscar Murillo. And a downstairs room gathers together all the coarsest and most eye-jabbing works in the show, mainly overwrought or hyperreal paintings involving creatures. (It is on the right as you enter.) But the proportion of duds in Mixing It Up is unusually low.

The manner of making is as diverse as the content. Paint is applied by airbrush, rags or fingers; there is faux-fresco, spatter, wash and drip; a kind of painting that shows all its own workings and a kind that seals over everything below the surface.

And so many paintings look backwards. Not just Brice’s exceptionally intelligent homages, but the lovely reprise of Piero’s Resurrection as a Calypso paradise by Tasha Amini and the paintings of Louise Giovanelli. Her diptych of two gleaming satin shirts is built up using Renaissance techniques, including the application of gold leaf beneath the paint. A portrait of Alfred Hitchcock’s muse Tippi Hedren, glancing sideways in something like open-mouthed fear, has the glacial flawlessness of a Gerhard Richter painting (there is, incidentally, a group of Richter’s austere graphite drawings in an adjacent gallery).

Nothing comes of nothing in art. No painter works entirely alone. What is so special about this particular lineup at the Hayward Gallery is precisely what unites these painters: their sincerity and integrity, none of them despising their medium, conceptualising its value, character or past, or using pigment for secondary purposes. That Rugoff could put on such an absorbing and dynamic exhibition even without involving so many other contemporary stars – Tomma Abts to Michael Armitage to name only the As – is a testament to the pure strength of these paintings.

• Mixing It Up: Painting Today is at the Hayward Gallery, London, until 12 December