Director Stephen Frears “accused me of that,” says the three-time Oscar winner, who squawks and trills on the big screen as Florence Foster Jenkins (in theaters nationwide Friday). Warbling her way through take after take, “I said, ‘You’re so used to me that you think it’s good! You’ve lost all sense of proportion!’ ”

In the period comedy, Streep embodies the real-life Florence Foster Jenkins, an ebullient New York heiress who in 1944 sold out Carnegie Hall off the novelty success of her unintentionally humorous opera recordings. As zealous about the arts as she was shockingly tone-deaf, Jenkins was affectionately egged on by her common-law husband and manager St. Clair Bayfield (Hugh Grant), who would buy up newspapers and pay off audience members to shield her from any criticism.

Who was the real ‘Florence Foster Jenkins’?

Like her recent musical turns in Stephen Sondheim’s Into the Woods and last summer’s Ricki and the Flash, all of Streep’s singing was performed live on Florence’s London set. But even with weeks of vocal coaching prior to shooting, the constant off-pitch screeching took its toll.

“I was talking to Renée Fleming and she said, ‘No one sings that aria more than twice a month,’ but I was singing it eight times a day,” says Streep, 67. Even more challenging was trying to keep her cool in the face of aghast reactions from Florence’s accompanist, Cosmé McMoon (The Big Bang Theory’s Simon Helberg). “The first music lesson was the hardest to get through because I’d laugh in the middle of it,” she recalls. “I’d see him react and just blow.”

Outbursts of cackling afflicted her co-stars, too. “There’s a scene where I had to be furious with the mockers and scoffers, and really, all I’m doing is trying as hard as I possibly can not to laugh,” says Grant, 55. “He’s imploding with rage, but I was imploding with laughter.”

But the guffaws ultimately come from a tender place, as Cosmé grows to admire Florence’s dogged spirit and dedication to her craft. “When you watch your own children or anyone’s children singing with such abandon, you don’t even consider having any criticism or notes for them,” says Helberg, 35. “You care so deeply about them and are protecting their joy, which is really what happens here.”

Meryl Streep stars as a New York heiress who dreams of becoming an opera singer.

Helberg played piano in jazz and rock bands as a teenager but says he practically needed to relearn the instrument in order to master Florence’s classical selections. Grant similarly cut a rug in the 2003 romantic comedy Love Actually but jokes that he dreaded hoofing it again in this film for a heavily choreographed dance scene midway through.

“You’re reading the script and suddenly it says, ‘Bayfield dances, and he’s brilliant,’ ” Grant says. “That takes a writer one second to type, while I’m in a bloody rehearsal room for three months with ladies in leotards learning to do the swing. But by the end, I quite liked it.”

Streep quips: “You can break it out at parties now!”