When Kleiser cast his leading couple, Travolta had already filmed Saturday Night Fever but it was not yet released – and he was largely known as the young heartthrob from TV sitcom Welcome Back, Kotter.

Newton-John was a pop music superstar, with several hit records under her belt.

“John and I both wanted Olivia, and she was resistant because she’d done a movie that didn’t do well in England, a sci-fi movie, and she thought she might be a little too old to play opposite him,” Kleiser says, referring to Toomorrow (1970).

“She requested a screen test and we did it. John and I both treated her like a little sister, gave her all the encouragement, and it worked.”

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Travolta and Newton-John have remained close friends over the decades, starring together again in 1983’s Two of a Kind, a flop by any measure, and reuniting in 2012 to make a Christmas album.

They swap text messages and have supported each other through dark times, including the death of Travolta’s son in 2009 and the return of Newton-John’s breast cancer after she had beaten it in the 1990s.

Kleiser says that while he has seen his stars separately over the years, an anniversary get-together at the motion picture academy in Los Angeles next month will be the trio’s first full reunion.

The director made other films after Grease – most notably The Flight of the Navigator (1986) – but the lure of big studio blockbusters lost its lustre and he moved away from the Hollywood system in the 1990s.

In a wide-ranging interview he spoke of his frustration with Barry Gibb’s lyrics for the film’s title track sung by Frankie Valli, which he thought struck an incongruously dark tone. Kleiser took Gibb aside and it emerged the Bee Gee knew nothing about the film, the screenplay or the stage show – and thought the word Grease was ridiculous.

“I spoke to him about changing the lyrics. I said, ‘There’s no serious themes in the movie,’ and he said, ‘Well, why don’t you shoot a serious scene so the lyrics will work?’”

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Kleiser believes the film’s longevity can be attributed to its universal themes, the chemistry between his leads and its appeal to our nostalgia for a more innocent age “where there were no terrorist attacks or shootings”.

“That all came together in a perfect storm and hit the public zeitgeist,” he says.

Travolta became a global superstar and his career highlights in the intervening years – another 30-plus films – barely need repeating.

After a lull in the 1980s, he underwent a resurgence sparked by an appearance in Quentin Tarantino’s 1994 masterpiece Pulp Fiction that made him an icon for a whole new generation.

Newton-John kept her music career going and went on to appear in Xanadu (1980) and Two of a Kind (1983).

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She says she still has the skin-tight black pants she wore in Grease.

Kleiser still goes to screenings but says he prefers these days to watch the audience experiencing and enjoying his crowning achievement.

“I see lots of flaws in it, but I think the flaws are part of the charm of Grease – the fact that it has a rough-around-the-edges feel,” he says. “It’s not real slick; everything is not perfect, but I think that adds to the feel of it.”