“Every day was a lesson in acting. It was like going to the best drama school ever for six months – and it happened to be on the beach.

“Johnny was very kind to me. He’s wonderful. He becomes Jack Sparrow and just lets it flow, and fall out of him. Geoffrey was so funny. I didn’t expect him to be. He’s a huge, big teddy bear.”

But Bardem, who plays the menacing ghostly pirate hunter Captain Salazar, intimidated Kaya at first.

“I thought he was going to be super-intense the whole time,” she says. “But he’s actually super-lovely, and fluffy and friendly in between shots.”

Kaya plays Carina Smyth, a gutsy scientist and astronomer who helps Depp’s Captain Sparrow search for the mythical Trident of Poseidon.

She navigates the pirates’ adventures while squeezed into crushing corsets and high heels, yet she says it was the male stars who moaned about their costumes.

“There was a day when all the men were complaining about the little heel on their boots,” she says. “They were going, ‘oh, these boots! My back is killing me.’ Big deal. Are you kidding me?”

Kaya had battles of her own with her tightly laced bodices and billowing gowns. “I had a corset and 17 layers,” she says. “The first day on set I thought, ‘how am I going to do anything in this dress?’

“I’m very much a jeans and T-shirt girl. But you adapt, and get your husband to slowly loosen it at lunchtime without telling anyone.”

Kaya’s husband is US actor Benjamin Walker, 34, who starred in 2012 hit Abraham Lincoln: Vampire Hunter.

They met in 2014 while filming action adventure The King’s Daughter set for release later this year. They married in 2015, and their son was born last November.

In this fifth Pirates, Kaya takes on the leading lady role originated by Keira Knightley in 2003. The pair share a pivotal scene in the latest movie, but they never actually met.

Instead, they were combined on screen digitally as Kaya was nine months pregnant when Knightley filmed her cameo.

“It was actually my due date,” Kaya recalls. “I was very heavily pregnant, so I wasn’t even there.

“There was a lot of camera trickery, so I never got to meet her, which I’m really sad about.

“I know she lives near me in London, so I’m going to stalk the streets and try to bump into her maybe.”

And if a sixth Pirates movie sails into her future? Kaya will gladly leap aboard. “I can only hope,” she says.

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