What if we didn’t meet the Beatles?

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The whimsical what-if comedy “Yesterday” poses the intriguing question: Had the Beatles never existed, would the world be a worse place to live?

Related: If you were a struggling singer-songwriter and you were the only person on the planet who knew those classic Beatles’ songs, would you fob them off as your own, ensuring fame, fortune and your place in the pop-cultural firmament?

The British actor Himesh Patel plays a musician in that precise ethical dilemma in “Yesterday,” wherein a brief worldwide blackout results in no one remembering who the Beatles were. Jack, Patel’s character, realizes something’s amiss when a reference to “When I’m Sixty-Four” sails over the head of his effervescently supportive manager Ellie (a curly-haired, chronically ebullient Lily James). Later, when he strums out a quietly mesmerizing version of the film’s title song, his friends compliment him on writing a terrific tune, with the caveat that “it’s not Coldplay.”

Such are the running gags that keep “Yesterday” aloft within a gently amusing speculative bubble, as Jack – who works at a warehouse store in the picturesque seaside town of Lowestoft – becomes an overnight sensation. When he tries to play “Let It Be” to his kind but distracted parents, they fail to recognize its greatness; it’s only when Ed Sheeran drops by – in one of the film’s funniest scenes – that Jack (along with John, Paul, George and Ringo) begins to get his due. “You’re Mozart, man,” Sheeran tells his new protege at one point, “and I’m definitely Salieri.”

For the first hour of its too-long running time, “Yesterday” keeps the balloon in the air, sending Jack on a giddy trip to stardom with the help of the real-life Sheeran and a hilariously insensitive L.A. manager played by Kate McKinnon, in all her cockeyed deadpan glory. Written by Richard Curtis – best known for the treacly holiday romcom “Love, Actually” – “Yesterday” evinces the screenwriter’s love-it-or-loathe-it sentimentality, which here starts out modestly enough until finding full florid expression in an over-sweet third act. Patel, who spends most of the movie scowling and looking anxious, has a simple, pure voice that perfectly captures the mix of naivete and virtuosity that beguiled the Beatles’ fans in the first place.

Eventually – perhaps inevitably – “Yesterday” overplays its hand, with Curtis seemingly at a loss for how to resolve a story that, after its initial premise has been mined for maximum humor and poignancy, has very few places to go. (Curtis’ solution is a maudlin, creepily literalistic scene suggesting that there are some cataclysmic losses it will always be too soon to revisit.) Although director Danny Boyle does his best to inject visual interest by way of canted camera angles and snazzy on-screen graphics, even the brightest visual design can’t overcome cliched chases through train stations and an improbably romantic moment beamed from the stage of a packed Wembley Stadium.

Of course, the entirety of “Yesterday” is improbable, so suspending disbelief is required from the jump, when it’s clear that the self-absorbed Jack is grouchily unaware of Ellie’s obvious unrequited love. That might be the biggest stretch of all in “Yesterday,” which at its least convincing inspires more than a few eye rolls, but at its best invites the audience, along with the characters on screen, to hear some of the finest songs ever written for the very first time.

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Two and one-half stars. Rated PG-13. Contains suggestive material and strong language. 116 minutes.

Ratings Guide: Four stars masterpiece, three stars very good, two stars OK, one star poor, no stars waste of time.

Advance for 9 a.m. Thurs June 27