Ahard rain falls on a glittering grey sea. Wind harries sullen clouds across low-lying horizons. Overcast skies shed a pale glare on the churned earth below. Thunder and gloom, turbid brown rivers, corn standing solid as a wall at the field’s edge beneath squalls of paint, thick as mortar. This is summer in John Constable’s England. Or, to be more precise, it is the season of late Constable (1776-1837), painted in the grief of bereavement. The Royal Academy’s stupendous new show may open with some early cloud studies and Constable’s The Leaping Horse, last of his so-called Six-Footers, but almost everything here was made after the death of his wife, Maria, in 1828. Constable was left to raise seven young children on his own, at the age of 52. He wore mourning for the rest of his life. The devastating oil “sketch” of Hadleigh Castle, for instance, was painted during her final illness. With its ruined towers and black birds circling in the chill white air above endless flatlands, this desolate vision is shot through with sorrow and fear. Its origins lie in a pencil sketch made even before he met Maria, as if a dark memory of life before her was suddenly resurfacing in this storm of turbulent brushstrokes. “I shall never feel again as I have felt,” Constable wrote to his brother, “– the face of the World is totally changed to me.” Like The Leaping Horse – in which river, rider, barge and horse are barely distinguishable up close in the mass of claggy paint – the sketch for Hadleigh Castle is entirely without precedent. Five or six feet wide, painted on canvases that were probably tacked to the studio wall, these so-called sketches are an amalgam of spontaneously veering brushstrokes that scarcely shape themselves to the scenes they describe. Constable worked on them for months at a time, saying only that they were not for public consumption, compared to the finished “exhibition” versions. They cost him dearly, made him nothing, and were never shown in his lifetime. But they are the essence of this show, which brims with art made mainly for himself. Dawn breaks as a needle of white paper in a swathe of dark ink. A woman below a tree melts like wax in seething brown oil paint. A sketchbook lies open, showing Constable’s watercolour of a Sussex chalk bank, newly eroded to reveal the spectacle of a human skeleton. In the Tate’s famous Salisbury Cathedral from the Meadows it is almost impossible to dredge the people and animals from the morass of liquid river: either as figures or just separate brushstrokes. These paintings are turbulent, agitated, staggering to behold. The eye inches over the surface as if searching for fossils in shale or shells on a beach, startled by every tiny incident. Everywhere you look there is some outlandish mark, as often made with a blade as a brush. The paint pools, sticks, butters the canvas, grazes the weave; it is viscous, slow-moving, dense, always strangely opaque. No matter what the titles claim – that this is Old Sarum, Flatford Lock or Brighton Beach – what you are looking at, before all else, is the mysterious behaviour and potential of paint. Late Constable never pretends to simple illusion. An almost comically candid notice next to A Farmhouse Near the Water’s Edge acknowledges that “the brushstrokes make the objects in this painting a bit difficult to see”. This is meant to reassure young visitors, but might do as well for adults faced with one of Constable’s most inchoate works. And there are a couple of other paintings in this show where the subject – a biscuit-tin cottage surrounded by hollyhocks, say – is far less interesting than the way it is made. People are diminutive, as lost in these landscapes as Wordsworth’s Lucy, ethereal heroine of the Lyrical Ballads, “half hidden from the eye”. Commissioned to illustrate As You Like It, Constable draws a tree flaring upwards; it is more or less impossible to distinguish the melancholy Jacques slumped among its roots. His commemoration of Sir Joshua Reynolds, dead president of the Royal Academy, shows only an empty plinth in a glade. Look at his quickfire sketch of Michelangelo’s Taddei Tondo, bequeathed to the RA when Constable was an academician, and you would scarcely know he was depicting a sculpture so much as spectres flickering like fire: a vision of motion, force and spirit. Constable tried and failed to become an academician year after mortifying year, snubbed every time. He was a student at the RA Schools in his early 20s, and consistently showed in the annual exhibition. But he was not elected until the approach of his 53rd birthday. The present show is a yet more belated recognition from the Royal Academy, therefore: its first survey since Constable’s unexpected death at the age of 60. Anyone looking at these late works can hardly help noticing what Turner liked to mock: the peculiarly conspicuous dabs, specifically of red, with which Constable indicates a dog’s tongue, a jacket, a distant figure. The difference between these two contemporaries is proverbial: in essence, dematerialisation versus its painterly opposite. But both were radical beyond anything ever known in English art. Stonehenge, painted by Constable, is a collection of tumbled rocks beneath the far greater phenomenon of the empyrean – the swooping, rushing heavens, all skywriting and radiant cloud. Two beams from outer space, as it seems, hurtle straight down to the centre of the circle: rainbows of brilliant light arriving from before ancient time. Dark rivers stir, black on black, in the enormous oil sketches. Look deeply, and every passage is crammed with sensation: the memory of damp undergrowth, the smoky chill of autumn, droplets sounding on still water. Yet none are specifically described. The cliche is that Constable prefigures modernism, specifically abstract expressionism. But his marks are so wild and fervent they make the Americans look orderly, even while remaining somehow figurative. And Constable can do this even on the least scale. One of the greatest works here is among the smallest, not much bigger than a paperback. It shows the sea far away across a beach, glowering and sparking beneath an oncoming storm. The horizon is scored in with the handle of the brush, the clouds rapidly pressed around the sky. It is a thrilling sight, heavy with doom, yet painted with superb precision. Until, that is, something breaks in the painting – and perhaps also in the painter. Black rain starts to rush down the surface in violent sweeps, as if the centre could not hold. But is it weather, or is it pure paint, and which do you see first – the exhilarating enigma of late Constable.