Directed by Mike Leigh. Starring Sally Hawkins and Eddie Marsan. Rated PG. Opens Friday, October 24, at the Cinemark Tinseltown

“You make your own luck,” someone says late in this invigorating new effort from British veteran Mike Leigh, and for once the famously skeptical director seems to agree. The title even suggests that happiness may have more to do with finding luck than the other way around.

This philosophizing is not readily apparent when we first meet Poppy (Sally Hawkins, in a career-making performance), a Camden Town gadabout with a Raggedy Ann fashion sense, a ready smile, a Cockney accent, and a penchant for supplying both sides of a conversation when strangers don’t instantly take to her whimsy. She may be a gangly, wild-eyed nutter of sorts, but she’s also a grade-school teacher with passion for her work and good relations with her colleagues and pals (including a stoical flatmate played memorably by newcomer Alexis Zegerman).

Poppy’s dauntless cheer is put to the test when—in a grab at growing up—she decides to take driving lessons. Her instructor (funny-faced Eddie Marsan) turns out to be a lit-fuse racist with conspiracy theories where his heart should be. Their jaunts around crowded London are tense marathons with worlds colliding at every zebra crossing. But Poppy isn’t out to prove anything. And Leigh—as usual, giving us the polished version of scenes he first improvised with his actors—is careful to show us his chattering heroine’s surprisingly soulful insights into the dark, if ultimately mundane, environment that produces such miserable people.

Along the way to poignantly wrapping up this wonderfully satisfying tale of teachers and students, there’s time for some very funny everyday stuff, including memorable Tuesday-night flamenco lessons with a teacher (Karina Fernandez) who tells her to approach life with ferocity; Poppy gets the point, but she’ll only fight if there’s a laugh in it as well.