In 1974, by reluctant invitation, a homeless but not vanless woman by the name of Mary Shepherd parked her banged-up vehicle in the driveway of the Camden Town home belonging to playwright, novelist and humorist Alan Bennett. A former concert pianist of shadowy circumstance, Shepherd was well-known as a vagabond in this rapidly gentrifying part of London. With a mixture of timidity, kindness, inertia and privileged guilt, Bennett let her stay on his patio. For 15 years.

The anecdote grew into a cottage industry. Bennett wrote about his neighbor in various forms: in a London Review of Books essay; in a 1999 play starring Maggie Smith, who re-created the role 10 years later for a BBC radio adaptation; and now, in a Bennett-revised screenplay hewing closely to his play, a film directed by Nicholas Hytner, who staged the theatrical version.

Smith again plays Shepherd, opposite Alex Jennings as the diffident, sweetly reticent Bennett. Or, rather, two Bennetts: In the conceit of “The Lady in the Van,” Bennett’s writing self and his “living” self are two separate characters, both played on film by Jennings. This allows Bennett to have polite but reproachful disagreements with himself, regarding Shepherd’s disheveled, mystery-laden life, lived just outside his window, and Bennett’s role in her story.

You can look at “The Lady in the Van” as a portrait of a changing urban neighborhood. Faced with Bennett’s depiction of variously grousy but ultimately supportive citizens looking out for the hard-luck soul in their midst, American moviegoers may experience unusually heavy doses of guilt themselves. Would we do the same in his circumstances?

Shepherd, apparently, was a genuine, needle-sharp wit and the way Smith plays her, the character’s tart rejoinders are superhumanly perfect. It’s a robust, unsentimentally funny turn. “The Lady in the Van” is also a self-portrait, and in Bennett’s shrugs of humane generosity, Jennings develops a characterization of sweetness and sadness in well-judged proportions. Bennett is writing about a man — himself, that is — whose ailing mother, near the end of her life, is far less central to his cautious existence than Shepherd was, for years.

Much of the material is witty and astute in its observations of the way the disruptive presence of Shepherd (and her various vehicles) affects the attitudes and everyday lives of Bennett’s North London neighbors. “We like to think we’re a community,” one of them says, though she’s plainly not happy about Miss Shepherd. Frances de la Tour and Roger Allam are spot-on as two other Camden Town residents. The musical score by George Fenton nearly kills what’s good about “The Lady in the Van,” small though it is, with its aggressively cutesy comic impulse. Smith and Jennings don’t require that sort of help.