MR. TURNER “Please, please. Mr. Turner was my father! Call me J.M.W.”

MR. TURNER sounds like the stuffiest period piece possible: Renowned landscape painter J.M.W. Turner, exceedingly British, dodders about the 18th and 19th century art world, obsessing over the way sunlight breaks through ocean clouds after a storm. On paper, the film has the makings of a creaky Merchant Ivory costume drama, full of florid speechifying and haughty glances in gloomy parlors. But in director Mike Leigh's hands, Mr. Turner does something singular and remarkable: It captures the role of the artist in his time.

Leigh, the director who brought us Topsy-Turvy and Vera Drake—and, more recently, Happy-Go-Lucky and Another Year—is known for observant, occasionally bleak films that mine tension and humor from the misunderstandings, expectations, and delusions that shade interpersonal relationships. In bringing his grounded, human-scale sensibility to bear on a historical figure, Leigh not only recreates the circumstances of Turner's life, but he also creates a context for understanding his work.

Turner was a Very Important Artist in an era when painters could achieve a level of celebrity that's nearly unimaginable today. His life bridged two centuries—he was born in 1775 and died in 1851—and his work spanned two movements, from the high-voltage Romanticism of storm-tossed ships at sea to fuzzy depictions of light on canvas that heralded the Impressionist movement to come.

Leigh knows that in order to understand how Turner's paintings were perceived at the time, we must also understand how the world looked when Turner was painting them. And so Leigh gives us a vision of London that's dull, colorless, and candle-lit—until we enter a pigment store, lined with jars bursting with vibrant color. In contrast to the drab London streets, these colors are viscerally satisfying, and we suddenly understand how people might have been moved by—and grateful to—an artist who'd given them something beautiful to look at. Throughout the film, Leigh's camera lingers on seashores and landscapes, forcing us to consider the same ephemeral variations of light and color that obsessed Turner.

But while Turner's paintings were, and remain, beautiful, his characterization in Mr. Turner is anything but. He treats the women in his life shabbily, from the maid he sleeps with when it suits him to the several illegitimate children he pretends don't exist. And he disingenuously maneuvers through the clubby, competitive art world, which Leigh entertainingly and accurately depicts as gossipy, backstabby, and a bit ridiculous—courting controversy even as he flinches from criticism.

As Turner, Timothy Spall—perhaps best known to Americans, however unfairly, as Wormtail from the Harry Potter movies—grunts and frowns his way through a remarkably complete, self-sustained performance. Spall's Turner exists. He's probably riding the #4 bus right now. If you ask him to move his hat off the seat so you can sit down, he'll scowl at you. Turner ages slowly over the course of Leigh's film, and as he does, he's forced to confront new technologies and fashions that present unprecedented ways of experiencing, and capturing, the world.

Richard Linklater's Boyhood was last year's big, ambitious cinematic experiment with time, but in its way, Mr. Turner is just as concerned with time's passage. Where Boyhood strode more or less triumphantly into the future, Mr. Turner is more interested in how time passes once you're finished growing up. Middle age drags on until one day you're old; old age drags on until one day you're dead. It's slow and inexorable and the people around you won't notice it's happening, until they do: Has he always looked so old? In the end, all that matters to Turner is that pigment and canvas will survive him—and for better and for worse, they do.