“Apologies for the shirtlessness,” says Tom Hiddleston. “I didn’t want to show off.” The world’s most impeccably spoken Marvel baddie is looking awfully embarrassed. I’ve caught him emerging topless from his trailer, late at night, with female company. The makeup artist has been in with him, carefully pawing at his torso. Hiddleston is shooting a movie in Hawaii and, as it is, his skin doesn’t look sufficiently sun damaged. Muddier stuff is slathered on, and our star is good to go.

This dramatic tan is part of the latest, and perhaps most adventurous, step in Hiddleston’s ascent to the A-list: the lead role in a grand new reboot of the King Kong franchise. It is why we are both standing in mud in the middle of the night on the Hawaiian island of Oahu.

The question arises, though: do we really need another movie about King Kong? Ever since the romantic giant ape landed in New York in 1933 with a giant crush on Fay Wray, he has cropped up in at least another six films, most recently Peter Jackson’s handsome 2005 remake. In the latest reincarnation, Kong: Skull Island, he is getting the origins treatment – his story beginning again, ready to be continued in future films. Reassuringly, any reservations one might have about such a project seem to be shared by the film’s producers, who chuck around words such as “fresh” and “current” as casually as Kong juggles biplanes.

“I went in and pitched a movie I would want to see and my friends would want to see,” says the director, Jordan Vogt-Roberts. “I honestly thought they were going to laugh me out of the room. Then they responded really well and we started building that story.”

One can understand this initial concern. The 33-year-old has just one full-length credit to his name: the low-key coming-of-age indie The Kings of Summer. The only thing that film has in common with this one is that trees feature. Vogt-Roberts also looks every inch the indie director – gold medallions, heavy hipster beard – not a guy you would automatically trust with a reported $190m (£152m) budget. But maybe it is because of his indie credentials that the vibe on set seems so relaxed. There is an army-like camaraderie between the actors playing soldiers and those playing non-military folk.

So what is the movie that Vogt-Roberts and his pals would want to watch? Well, it’s set in 1972: the Vietnam war is almost over and the Landsat programme is dawning. For the first time, satellite imagery is able to capture the Earth as a whole and shine a light on previously unknown areas. A voyage to discover what really lies on a mysterious island is launched with a ragtag crew, all with conflicting missions.

Jordan Vogt-Roberts on the set of Kong: Skull Island with Tom Hiddleston. Photograph: Chuck Zlotnick/Warner Brothers

“In the early 70s,” says Vogt-Roberts, “the world was in chaos, and I love the idea of using that as an access point for the characters, taking people who are in the middle of sexual revolutions and racial riots and losing wars for the first time and political scandals – people who are watching the world crumble around them – and sending them to an island untouched by man. There’s a sense of catharsis to that.”

But don’t be fooled by the film’s vintage feel. The producers are keen to position this as a contemporary adventure. Recruiting Hiddleston, hot off award-winning TV show The Night Manager, is indicative, and he is surrounded by an eclectic and self-consciously contemporary ensemble. There is 2016’s best actress Oscar-winner Brie Larson, franchise addict Samuel L Jackson, character actor John C Reilly, Straight Outta Compton breakouts Corey Hawkins and Jason Mitchell, plus John Goodman, fresh from his terrifying turn in 10 Cloverfield Lane.

“It’s a pretty big family to be travelling around the world with,” Larson says, mid-midnight snack. We are in an open air tent and she is ploughing through salad, surprisingly energetic and awake. She has just done the umpteenth take of one especially draining scene; there are many more to come. “Usually, I’d be done by now,” she says with a grin. “Most films I’ve done are 20-, 30-day shoots. So I keep thinking this is the end and we’re not even a quarter of the way in.”

To create a place of unique otherworldliness that could conceivably exist on Earth, three locations – Australia, Vietnam and Hawaii – are being amalgamated. There is an emphasis on bricks–and-mortar sets rather than a CGI overload, which is reserved for the big man himself (a Kong record height of roughly 85ft/26 metres) and a host of nasty creatures with whom he shares his ecosystem. “Jordan always insisted that we should be in real places,” Hiddleston says. “There should be as little soundstage or green-screen work as possible. He was location-scouting for nine or 10 months.”

Jason Mitchell in Kong: Skull Island. Photograph: Warner Brothers

Despite the hour, he is animated and enthusiastic as he talks to me between takes. This scene involves the characters arguing over whether Kong is friend or foe. It is intense, but what is initially thrilling to watch from the wings becomes notably less exciting the 30th time round. While Hiddleston and Larson remain upbeat (she does an improvised workout with a prop gun whenever the camera stops rolling), Jackson is starting to feel the strain. “How many times have we done this?” he asks. No one seems to know.

When it comes to my chat with him, I’m gathered with a handful of other journalists and his weariness seeps through.

“Why do you think this King Kong is different from the other King Kongs that we’ve seen,” asks one journalist. “I don’t know. I haven’t seen it,” replies Jackson.

“When we spoke to the director and the other actors, they compared your character to Captain Ahab. Is that something that inspired you too,” asks another. “No,” says Jackson.

Still, at least Jackson made it to Hawaii this time. In 1992, he was due to head here to film his doomed role in Jurassic Park when a hurricane destroyed the set before his scenes were shot. His work on Steven Spielberg’s dinosaur thriller was consequently based in LA. His biggest challenge for both projects, he reports, remains the invisible co-stars.

“The first lesson I got on green screen was from George Lucas years ago: the more you do, the more we have to draw,” he says. Do the practical sets help? “No, because you still have to ask the same questions. How big is it? Where is it? How fast is it moving? Sometimes they don’t have the answer to that.”

Film still from Kong: Skull Island. Photograph: Warner Brothers

At least his Avengers co-star is living and breathing, right? “Tom’s got his fans,” he says with a smile. “A lot of girls. It’s good to work with people you know and trust. I guess he’ll be going back into the Marvel universe and put that green suit on again. Hopefully, I’ll be back with my eye patch and we’ll be together again.”

The love is mutual: Hiddleston waxes on about how Jackson is “a consummate professional … just a very fine actor”. But that, surprisingly, is about it when it comes to romance in the film. Despite Kong’s penchant for women, in this version, he is all business, no pleasure.

“This is not a traditional Beauty and the Beast story,” says Vogt-Roberts. “I personally don’t want to see a damsel-in-distress story and I don’t think the rest of the world really wants to see that any more.”

This was a deal-breaker for Larson, too, who added tenacity to a victim narrative in Room and will next be squaring off with a warehouse full of gun-toting blokes in Ben Wheatley’s Free Fire. “We’re in a really interesting time when we’re interested in seeing something different,” she says. “I’ve seen women who have found their way to continue to be feminine but still exert a sense of force and a sense of strength, and that’s important to me.”

Kong: Skull Island, then, is dodging some familiar tropes. But it is also part of a very modern trend: not just a kickstart to one dusty franchise, but a way of breathing life into a shared universe, a world also inhabited by another giant of the screen: Godzilla. The breadcrumbs have already been dropped online, and there are easter eggs in the film to reward the hardcore monster fans. But, on set, everyone is tight-lipped about the upcoming face-off, scheduled for 2020.

“I don’t know much about it,” Hiddleston says. “We’ve got to finish this one. I obviously know it’s a plan and that’s what Legendary [the company in charge of both properties] wants to do. It’s exciting and something that hasn’t been done in a long time. If it’s done in the right way, then it could be cool.”

Godzilla 2, with its rather leading title, King of the Monsters, is next, with Millie Bobby Brown of Stranger Things attached. Might a Kong sequel be on the way, too? Vogt-Roberts shrugs off talk with a lightness befitting his roots, rather than his reality: “That’s a little bit above my pay grade.”

• Kong: Skull Island is released in the UK on 10 March.