A bit of graffiti is briefly glimpsed in this film: Ape-ocalypse Now. The comparison isn’t entirely off. There is a shaven-headed military renegade leader who’s had a terrible moment of clarity about the human condition, and whose command is about to be terminated with extreme prejudice. But in fact this latest exciting and impressive episode in the Apes franchise – directed and co-written by Matt Reeves – is closer in many ways to old-school war movies and POW dramas like The Great Escape or Bridge on the River Kwai, and the rangy, dystopian-future pictures of the 60s and 70s such as, of course, the original Planet of the Apes.

The continuingly absorbing Apes franchise delivers its stories with conviction and intensity; it is utterly confident in its own created world, and in the plausibility of its ape characters, who are presented quite unselfconsciously and persuasively. The movie isn’t afraid to place its centre of narrative gravity within this simian world, and does not feel the need to balance them all the time with humans. It has sweep, fervent ambition, some great action and combat sequences, sparse but nicely judged touches of humour and is also unafraid of long dialogue scenes and character confrontation. In moments of crisis, there are some compellingly strange extreme closeups on faces.

Part of the film’s potency derives from the figure of Caesar, the ape leader whose presence is created in motion-capture by Andy Serkis. His face is in fact quite unlike Serkis’s, but this figure has real presence and personality: a grizzled old soldier, whose mouth is always turned into a severe scowl of authority. Reeves gives him a classic travelling-shot moment from his point-of-view, the general walking through his encampment and the soldiers under his command instinctively rising and backing away in respect.

The situation is that humans and apes are now in open conflict: Caesar leads an ape community in a fortified forest from where he is about to retreat to a rumoured promised land: a paradisical valley with abundant food and water supply. He sees off an attack from humans, who have as servants certain quisling apes, former followers of Caesar’s traitorous ex-comrade Koba (a motion-capture performance from Toby Kebbell). The humans, themselves deeply divided about how to handle a growing virus which is depriving of them of the power of speech and reducing them to the status of animals, dismiss Caesar’s offer of a peaceful deal in which his simian kind will keep to the forest, and make a grotesquely violent attack, masterminded by the sinister Colonel, played by Woody Harrelson. His initial face-off with Caesar is edge-of-the-seat stuff. From there on, Caesar is on a rescue and revenge mission.

Perhaps it is absurd to attribute charisma to a character who is an amalgam of digital fabrication and flesh-and-blood reality but that is what Serkis/Caesar has: he genuinely does look like a careworn military leader, bowed by age, coarsened by violence, haunted by loss, but still physically strong and with a natural aptitude for command. It is a war movie rather notionally, in fact — closer to a quest movie, as Caesar and his few remaining stalwarts and disciples, including a slightly Golem-type ape, make their way across country on the way to their showdown with the humans who seek to enslave all of them.

War for the Planet of the Apes has its own sense of purpose; it does not get distracted with tricksy or self-aware Statue of Liberty moments, either ones of their own or variations on the original, and of course this is partly because of the franchise’s prequel status. But it is also clearly a larger decision to frame the movies with clarity and directness, without huge cosmic ironies. It’s an engrossing, forthright adventure.