The British film-maker Paul Greengrass and the Hollywood film star Matt Damon are sitting in a suite at the Corinthia hotel in central London talking about the opening scene of their new film, a bruising fight in the punishingly visceral style for which the pair have become justly celebrated.

“We shot that scene, that first fight, on the first day and it was like, we’re doing this,” recalls Damon. “It won’t be said that we came to pick up a pay cheque. We’re going to give it absolutely everything we have.”

Fifteen years ago, when Damon had just turned 30, he signed up to make an intriguing thriller based on a Robert Ludlum novel about a mysterious trained killer suffering from amnesia and in the grip of an identity crisis.

He had just done several films, including All the Pretty Horses and The Legend of Bagger Vance, which had turned out to be box-office flops. There were problems with the thriller. It was held back from release. There were reshoots and the editing process was fraught and lengthy. Seldom good signs. But in the event The Bourne Identity was pacey, atmospheric and it seemed to strike an emphatic chord in the uncertain days of the post-9/11 era.

It was a one-off film. Damon had not signed up for another. But owing to popular demand, as they say, another was made, and then another, and a series was born that so far has taken more than $1.2bn at the box office.

A great deal of that money was generated by a partnership that Damon went on to form with Greengrass. A one-time journalist who co-wrote the stunning exposé of the secret services, Spycatcher, with Peter Wright, Greengrass was known in British television for gritty realist dramas such as Bloody Sunday.

But he was an unknown quality in Hollywood. On the face of it, giving him a $75m budget was something of a gamble. Yet The Bourne Supremacy confirmed that Jason Bourne was a modern-day rival to that other JB – James Bond – only tougher, more troubled and completely unbothered about whether his martini was shaken or stirred.

The pair reunited a couple of years later for The Bourne Ultimatum, which was a massive worldwide hit. These films were tense, earthy and psychologically dark. Together, they created a global audience of devoted fans. With their astonishing fight scenes and taut, near speechless main character, they set a new standard in action films to which the 007 franchise, with a muscled-up Daniel Craig, felt compelled to respond.

Hang on a minute... Matt Damon in The Bourne Identity. Photograph: HO/Reuters

But by the time the $442m-grossing Ultimatum hit the screens in 2007, both Damon and Greengrass felt the drama had run its course. As Greengrass later put it: “I discovered in my heart I didn’t have another one in me.” Damon was even more conclusive: “We have ridden that horse as far as we can,” he said. “For me, I kind of feel the story that we set out to tell has now been told.”

However, Hollywood abhors a vacuum, particularly when it comes to highly lucrative franchises, and Universal, the studio that owned the rights to Ludlum’s character, had to produce a Bourne movie or lose its option.

So a fourth film was made, The Bourne Legacy, that contrary to the title’s implicit promise didn’t feature Jason Bourne or the actor, Damon, who played him. Instead, the lead character was called Aaron Cross and was played by Jeremy Renner, but otherwise the plot dynamic was so similar as to make you almost forget that Aaron wasn’t Jason.

It was a little as if a James Bond had come out with the lead character as 006. Although it did OK at the box office, it was a couple of hundred million dollars down on its predecessor. Nevertheless, Damon remained insistent that he wasn’t going to do another Bourne unless Greengrass directed and Greengrass was equally insistent that he wasn’t going to make another one.

But this is the movies and when someone makes a definitive statement like that, you just know the next scene will show them doing the opposite. So here we now are with a new Jason Bourne film called, with Ronseal-like literalism, Jason Bourne. And here are Greengrass and Damon sitting back with a look of satisfaction, a tough job completed, listening to me read out all their past quotes about not doing another Bourne film. What happened to their previous stance of no going back?

“Shall I answer that one?” asks Greengrass who, in his black T-shirt and long silver hair, has the look of a man who is about to enjoy an extended period of relaxation.

“Sure,” says Damon.

“Well, all that was true,” Greengrass says.

“Yeah,” says Damon, suddenly keen to chip in. “I want to just say that at the time I said that, that was true.”

Greengrass explains that it was Damon and his editor, Christopher Rouse, who co-wrote the script for Jason Bourne with Greengrass, who persuaded him that there was a film to be made. What changed Greengrass’s mind was the realisation that the world had changed. The earlier films aimed to be relevant to the global reality of the time in which they were made, in particular, the “war on terror”.

He thought a new reality could be reflected in a new Bourne film. So we see a Julian Assange-type character and a Facebook-type company and the post-Edward Snowden world of super-hackers and governmental surveillance.

Damon with Julia Stiles as Nicky in The Bourne Supremacy. Photograph: Jasin Boland/AP

But that still leaves the question of Bourne himself. The world may have changed, but has he? We last saw him having recovered his memory and learned the full truth of who he was and what he had done. Surely he wasn’t going to have a whole other identity crisis? How many times could he forget who he was?

“Yes, you couldn’t cheat on that idea,” says Greengrass. “I remember looking at the poster for Ultimatum at Oxford Circus tube. It said, ‘I remember. I remember everything.’ And I thought, ‘Well, I’m done. He remembers everything. That’s it.’”

“You said,” recalls Damon, “‘The second you hear him say, “I don’t remember”, that’s bullshit, I’m not doing that again.’”

“So it had to be something he did remember but he doesn’t understand. It’s like the old Guardian advert,” says Greengrass, referring to the famous 1986 ad in which a skinhead looks like he’s a mugger but turns out to be a saviour.

Both men are keen Guardian readers and the newspaper features prominently in The Bourne Ultimatum. Indeed, although we had limited time for our interview, Greengrass and Damon seemed more interested at first in discussing the plight of the Guardian in an age of free internet content. It was all I could do to get them back on to the subject of the film.

Damon is a natural communicator. I watched him for a while before our interview started, chatting to a number of people from the film company. Andy Murray had just that moment won Wimbledon and he told them an anecdote about Murray’s tailor that was done in a way that was very much “we’re all just normal guys shooting the breeze”.

Obviously, a big part of his on-screen appeal is a kind of heightened normality. It’s a deceptively ordinary kind of charm – not handsomely ironic like George Clooney or youthfully dangerous like Leonardo DiCaprio – but he has the ability to tether an extreme scenario in a recognisably human condition.

Bourne’s vain attempt to stop a Guardian journalist from being shot in the head during a set piece from The Bourne Ultimatum. Photograph: Moviestore/REX/Shutterstock/Rex

Paul said early on, you have to look like you’ve suffered. And the only way to do that is to suffer Matt Damon

It’s that formula that made The Martian work so well, bringing another world back down to Earth. And it’s one of the things that prevents Bourne from seeming like just a tight-lipped killing machine.

But if Damon trades on an everyman accessibility, there’s nothing everyday about the demands required to get in shape for the role of Jason Bourne.

“Oh, oh,” says Damon, now looking a little less toned than Bourne’s fat-free super-being, with a pained expression. “It was absolutely a different experience. Paul said early on, ‘Look, if we open the film and in the first frame of Jason Bourne we see your face and you look like you’ve lived well these past 10 years, we do not have a movie. You have to look like you’ve suffered. And the only way to do that is to suffer.”

That suffering meant two 90-minute high-intensity gym sessions every day for 10 weeks going into the shoot. And he could eat only vegetables and protein for months on end.

“Brutal,” nods Greengrass. “It was a statement of intent. Sadly, he had to make it.”

They both burst out laughing. There’s clearly a lot of mutual admiration and joshing between them. I ask them what they like about working together and there’s a pause.

“Silence,” says Damon, looking across at Greengrass.

“No,” replies the director. “I’ll tell you. Making a film, every film is a big gamble, large or small. The more that you do it, the more you’re aware of that. Relationships of trust and respect are hard to find. We hadn’t worked together in some years and then we came back on and suddenly there was that feeling that as a film-maker you’re not on your own. You can come on set some days and feel, ‘I don’t know about this’. The anxieties are very profound. That’s why it’s such a stressful undertaking. When you’ve got someone like Matt who’s going to sell it for you, who’s going to be brilliant and is committed, the feeling of empowerment is so intense. And love. He’s a fantastic man to make a film with. And we’ve been in the trenches before. We’ve been in the deepest shit that it’s possible to be in on a film set.”

They both speak of the experience of making The Bourne Ultimatum like war veterans recalling a particularly attritional campaign. The problem, which turned out to have a long afterlife, was that they were working on an uncompleted script.

Firing on all cylinders: a scene from the new movie, Jason Bourne. Photograph: Planet Photos/Universal

Damon explains: “You start trying to shoot the stuff you think does work while trying to fix the other stuff. It means a short day of filming is 12 hours. On top of that, you’re going out to dinner and writing. We had a conversation, I’ll never forget, in Madrid. It was three or four in the morning. We were standing in this street and we look at each other and go, ‘We’re in the wrong country. There’s nothing else we can shoot here.’”

Damon accused Gilroy of taking a ‘boatload’ of money and handing in an ‘unreadable’ script

They were working with an unfinished script because Tony Gilroy, who wrote the first two Bourne films, had apparently done a deal for the third film in which he only had to submit a first draft of the screenplay. And there was no after-service or further debate.

The situation left a bitter taste with Greengrass and Damon. Some years later, when Gilroy wrote and directed The Bourne Legacy, Damon gave an interview in which he tore into him. He accused Gilroy of taking a “boatload” of money and handing in an “unreadable” script. “I mean,” he said, “I could put this thing up on eBay and it would be game over for that dude. It’s terrible. It’s really embarrassing.”

It’s not done in Hollywood for the talent to diss the talent and Damon is definitely not the type to break the rule. As one top producer asked at the time, what happened that made “the nicest guy in town blow his stack”?

Damon quickly issued an apology, explaining that his feelings had been hurt and he was wrong to speak publicly because it was “stupid and unprofessional and just kind of douchey of me”.

But it was a revealing episode. Obviously, behind Damon’s usually affable exterior, something about Gilroy had really got up his nose. So when I ask them what they thought of Gilroy’s Legacy, starring Renner, there’s a pregnant pause before Greengrass turns to Damon and says with knowing laughter: “Do you want to take that one?”

Damon is unflustered, back on script and able to present a suitably diplomatic answer with what sounds like perfect humility. “I think in retrospect,” he says, “I understand very clearly why everyone did what everyone did.”

He goes on about the bind that everyone was in and how the best answer available was Gilroy’s. I suggest that it diluted the purity of the idea, having another quasi-Bourne running around beating the crap out of everyone. He doesn’t disagree but it’s not a topic he’s desperate to get into in depth. So is this other rogue ex-government agent set to continue?

They don’t know, they say, which sounds to my ears like: not just yet. Both of them are insistent that they are entirely in sympathy with the studio. If there was ever a disagreement with the suits, they are now firmly back on the side of Hollywood.

Greengrass in particular wants to dispel what he sees as the myth of Hollywood executives getting involved where they’re unwanted. Instead, he argues, that is a much more common experience in Britain.

“The idea that they approach that issue in a top-down way is the exact reverse,” he says. “That’s the problem with TV over here [in the UK]. The executives over here are way, way too empowered. The average director’s experience in British television is to get notes in an email from someone who they’ve never even met telling them in the most minute detail what to do. I’m glad I don’t work in TV over here because I wouldn’t be able to cope. I’d fall out with them all.”

With this the fourth Bourne – or fifth if you include Legacy – Damon and Greengrass were determined to avoid the stress that saw them through Ultimatum.

“The thing about making these films,” explains Greengrass, “is that they’re not like a normal film. With a franchise movie, it’s got to turn the wheels of the industry and the studio has to have them. So you start with a release date. They say we’re going to make a new Bourne film and it comes out summer of X. Then they start on a script and invariably the script is not ready in time.”

To get around this – as it’s known technically – arse-upwards approach, Greengrass and Rouse wrote the script before filming started on Jason Bourne. It’s fair to say that they didn’t take the Quentin Tarantino approach to dialogue. Damon speaks less in this film than he has done in any other Bourne movie. He makes Clint Eastwood in his spaghetti westerns seem positively loquacious.

It calls for a particular kind of acting that isn’t obviously expressive. I ask Damon what it’s like working on a film for months on end when your main interaction with other actors is hitting them.

“Well, I’ve done it three times. In the first movie, the Marie Kreutz character [Bourne’s girlfriend, played by Franka Potente) is still alive, so Bourne has a sounding board and he’s more confused about who he is and a lot more chatty. Once she dies in the first act of the second movie, it’s really a very lonely character. And we talked about that mostly on the second one. I remember Tony writing me an email saying, ‘You do realise what this means? You do realise you’re not going to talk in this movie.’ I said, ‘No, I love that.’”

He says that this time around Greengrass called him after looking at the finished movie and told him he only had about 25 lines in the whole thing.

Greengrass, however, believes that Damon packs a lot of feeling into his non-verbal acting. “I think what makes a Bourne movie is the violence and the set pieces,” he says, “but there’s a tremendous amount of emotionality in the character.”

He likes to cite the example of the scene at the end of The Bourne Supremacy in which Bourne goes to see the daughter of two people he had killed while under the drugged-up influence of a secret US counter-intelligence mission.

Jeremy Renner and Rachel Weisz in The Bourne Legacy, Tony Gilroy’s directorial contribution to the series. Photograph: Allstar

“When you think about that from an acting point of view, the proposition that he’s got to go to this young woman whose parents he murdered and he’s got to say ‘I’m sorry’, and he’s got to do it in a way that you buy that he means it, but [he’s] also got to do it so that you feel Bourne’s pain. You’ve got to sell two things that are absolutely contradictory but are truthful and that’s incredibly hard. And I think you absolutely do feel his shame and guilt but you totally believe he’s genuine. Even though it’s absolutely preposterous.”

Damon laughs at the idea of it. “The person who’s really suffered the loss is the girl! And he’s going there telling her how bad he feels about it.”

“But you don’t feel that,” says Greengrass. “There’s a vernacular to these films in terms of the acting that is really hard, because it is a heightened reality, it isn’t real life, but it’s got to feel emotionally truthful. When I think of a Bourne movie, unlike the other franchises alongside it in the summer, it feels to me it has to have that combination. I want to think we show the competition a clean pair of heels. I think our action is inventive, cooler.”

The action in Jason Bourne is certainly inventive, but it also feels a little too large, like that of other summer blockbusters, only better filmed, more realistic. Greengrass rejects the proposition but there is a sense that up against the CGI of superheroes, there is a need to make Bourne superhuman and the action overblown.

Some of the psychological complexity has been lost and with it some of the tension that made the earlier films so compelling. However, you sense that the fans will lap it up. And it will only serve to increase the appetite for a follow-up. Interestingly, without making it too obvious, Greengrass has painted the series out of the corner it was trapped in.

“That was one of the pleasures of it,” says Greengrass, “making the franchise live 10 years after and giving it possibilities without it feeling like a corny ending.”

So does that mean they’ll make another one together?

“Paul always says that the worst time to ask that question is right after you’ve made one,” replies Damon.

“I’m not going to make the mistake of saying ‘never’, like I did before,” says Greengrass. “But I’m not going to be sitting around. I’ve got other films to make.”

He wants to film a new version of Nineteen Eighty-Four, but he’s not sure yet if that’s going ahead. Damon has already made another film, with Alexander Payne, writer-director of Sideways and The Descendants, a social satire he describes as “the absolute opposite” of Bourne.

Damon is 45 now. How much longer can he endure the age-reversing regime of double gym stints and extreme diets?

“My guess is it will be a while before we’ll even get around to doing another one. They might reboot me before I bow out,” says Damon.

Greengrass seems to ponder the idea. “It’s got to continue,” he says.

Like a previous action hero, Bourne will be back.

Jason Bourne opens in UK cinemas 29 July