As he did back in 1999 with “Topsy-Turvy,” his film about the making of “The Mikado,” writer-director Mike Leigh has applied his idiosyncratic creative process—combining long bouts of research-based improvisation with eventual condensation—to a historical subject, in this case the last twenty-five years in the life of the great English landscape artist J. M. W. Turner. Once again the result is extraordinarily perceptive, and while it’s inevitably less immediately engaging than the story of how a Gilbert and Sullivan masterpiece came to exist, it’s no less revelatory.

The film is grounded not only in the writer-director’s concern for detail—an obsession clearly shared by production designer Suzie Davies, art director Dan Taylor, set decorator Charlotte Watts and costume designer Jacqueline Durran—but in the work of Dick Pope and Timothy Spall. The former’s cinematography doesn’t try to mimic the style of Turner’s proto-impressionist paintings, but it’s remarkable in its own way, capturing the look of England in the second quarter of the nineteenth century with uncanny verisimilitude. He and Leigh don’t elect to focus overmuch on Turner’s canvases; instead they recreate what the artist would have seen and what excited his imagination, and show the reaction to his work in the eyes of others, like the young John Ruskin (Joshua McGuire), who remained a defender even as Turner moved toward a level of hazy abstraction that puzzled and antagonized both the painter’s colleagues and the public at large—a hostility dramatized well in the film’s later stages.

It’s a reaction that is reflected beautifully in Spall’s mesmerizing performance as a gruff, charmless man whose obsession to express an inner vision took absolute precedence over any consideration of popular taste or social graces. In Leigh’s film he appears, around 1826, already fully formed—a rumpled bear of a man tramping about England—and the continent—in search of scenes that pique his interest. Returning home to London after a trip to Belgium, he greets his elderly father William (Paul Jesson) and Hannah (Dorothy Atkinson), the sad-faced housekeeper who also serves his manly needs without murmur, with as much warmth as he seems able to muster—which is not much—before lumbering into his studio to resume work by furiously attacking a canvas. He’s no more agreeable when he bursts into the Royal Academy in bulldog fashion, grunting dismissively at the pieces by other artists, including the decorous John Constable (James Fleet). When Benjamin Haydon (Martin Savage), a painter of biblical scenes who’s fallen on hard times, beseeches him for help, he offers it only grudgingly. And when his erstwhile mistress Sarah Danby (Ruth Sheen) makes an unannounced visit with the two daughters Turner refuses to acknowledge, one already with child herself, Turner treats them all unfeelingly.

And yet as everyone already knows from his paintings, this is no brute. When spending time at the estate of a patron, Turner can control himself, even become communicative. He’s moved by another guest’s piano playing, even going so far as to attempt to croak out a Purcell aria from “Dido and Aeneas” in time to her keyboard rendition (though she does have to correct some of the words). He shows fascination with the scientific inquiries of his friend Mary Somerville (Lesley Manville), and with the new technique of photography when he sits for a daguerreotype in the shop of John Mayall (Leo Bill) and is enthusiastic over the result, though he expresses thanks that at least it doesn’t involve colors.

Most revealing, however, is the friendship he develops with the Booths, Sarah (Marion Bailey) and her sea-captain second husband (Karl Johnson) when he takes a room with them under an assumed name while visiting the seaside town of Margate in search for new vistas to paint. After Mr. Booth’s death, Turner and Sarah grow ever closer, and he spends a good deal of time in her home, eventually even dying there.

Spall conveys all the aspects of Turner’s complicated character in a formidable performance that presents the artist both as a virtual force of nature and as an intensely driven and troubled man. The rest of the cast work in his shadow, just as those around Turner did in real life, but one must especially single out Atkinson, who brings enormous poignancy to the stooped, submissive Hannah, and Bailey, whose canny performance suggests the homely presence that apparently served as balm to the painter’s wounded spirit in his last years.

But if “Mr. Turner” is largely Spall’s and, through him, Turner’s show, it’s also Leigh’s, cementing his position as an artist who uses a unique method to bring to vivid life stories—whether jauntily humorous or deadly earnest, whether of the nineteenth, twentieth or twenty-first century—that carry the ring of emotional truth. This is one of the finest films about an artist ever made, fashioned by a filmmaker who’s a notable artist himself.