LONDON.- In Jez Butterworth’s new play, we — the audience and protagonists alike — are kept waiting and wondering.

It’s the summer of 1976, and Britain is in the midst of a heat wave. In Blackpool, a seaside town in northwestern England, three sisters (Jill, Ruby and Gloria) are reunited in the guesthouse that had been the childhood home, because their hotelier mother, Veronica, is dying of cancer. They must decide whether to put her out of her misery with a high dose of morphine or to let her continue to suffer.

A fourth sister, Joan, had emigrated to the United States 20 years earlier to launch a music career and hasn’t been in touch with the family since. Will she come home now? Why did she cut contact? Well, she had her reasons.

“The Hills of California,” written by Butterworth (“The Ferryman,” “Jerusalem”) and directed by Sam Mendes (“The Lehmann Trilogy”), runs at the Harold Pinter Theater in London through June 15. Rob Howell’s impressive set makes the most of the playhouse’s nearly 40-foot grid height, with three flights of stairs leading up to the unseen guest rooms.

The action unfolds on the first floor, where an endearingly tacky bamboo drinks bar and large metal jukebox imbue the cheap-and-cheerful Blackpool stylings with a quiet, sentimental dignity. The hotel is called the Seaview, but you can’t actually see the water from its windows. The dialogue is zippy, the humor sharp, dark and irreverent. A minor character sets the tone in an early exchange with Jill: “How’s your mother? The nurse says she’s dying.”

At several points, the set rotates to show us the hotel’s kitchen quarters, and we are transported back to the 1950s. We see the sisters as teenagers (played by four younger actors), under the rigorous if somewhat domineering stewardship of their mother, Veronica (an imperiously poised Laura Donnelly), who trains them up as a song-and-dance troupe. They rehearse songs by the Andrews Sisters, as well as the 1948 hit by Johnny Mercer and the Pied Pipers that gives the play its title. (The music is arranged by Candida Caldicot.)

Veronica is desperate for the sisters to play the London Palladium, to make it big and escape a life of drudgery in Blackpool, and the story pivots on an ill-fated audition with an unscrupulous talent scout (Corey Johnson), which holds the key to Joan’s long absence and estrangement.

Each of the sisters brings a distinct perspective and temperament to their predicament. Gloria (a boisterous Leanne Best) is gung-ho and outspoken; she harbors a deep resentment toward Joan, even suggesting that the stress caused by her absence brought on their mother’s cancer. Ruby (Ophelia Lovibond) is still in Joan’s thrall and just wants everyone to get along. Quiet, self-possessed Jill (Helena Wilson), who has stayed at home all these years and lately looked after Veronica full time, is the real star. She’s unworldly, a little uptight and not used to having her say — at one point she tells herself off for “waffling” when she has only been speaking for a matter of seconds — but her moral intelligence holds the play together.

“The Hills of California” has striking echoes of Harold Pinter’s 1964 play, “The Homecoming,” in which three adult brothers reconvene at their childhood home under the auspices of a brooding patriarch. In that play, too, one of the siblings has done well himself in America, and his relations with his family are a mystery to be solved.

Whereas “The Homecoming” was noted for its claustrophobic machismo, here it’s the women who dominate the proceedings, vacillating between sisterly tenderness and bitter recriminations.

Aside from the talent scout, the male characters in the play are conspicuously nice. Gloria and Ruby’s partners, Bill and Dennis (played by Shaun Dooley and Bryan Dick), are passive but dependable, vaguely hapless guys whose shortcomings are affectionately played for laughs: A penchant for silly voices in Bill’s case; chronic dullness in Dennis’. When the women’s discussions become awkward, or fraught, the men have the good sense to make themselves scarce.

We never see Veronica once she has grown old (she’s resting up in one of the bedrooms the whole time), yet she looms all the larger for her absence. In the 1950s scenes, she cuts a complex, and even somewhat sympathetic, figure. A well-meaning, pushy parent trying to live vicariously through her children is nothing new, but there’s a particular, tragic beauty in the terrible force of Veronica’s determination and her obsessive fixation on American showbiz as a lodestar of future happiness. (She tells her daughters: “A song is a dream, a place to be, somewhere to live.”) The guest rooms of the Seaview are named after U.S. states — a minor detail that carries so much pathos.

The denouement, when it comes, provides only a strange and messy sort of closure. There is no through line here, no moral lesson as such; just the chaotic, meaningless interplay of life force, personalities and contingency. Sometimes, that’s plenty.

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‘The Hills of California’

Through June 15 at the Harold Pinter Theater in London; haroldpintertheater.co.uk.

This article originally appeared in The New York Times.