Steve McQueen’s five-movie series for the BBC, Small Axe, only gets more thrilling and captivating with the appearance of this new episode at the New York film festival. He is setting new gold standard for drama – and cinema – on screens of any size.

Red, White and Blue is the true story of Leroy Logan (played by John Boyega) a black British man who in the 1980s abandoned a career in research science to become a police officer, despite – or in some agonisingly redemptive sense, because of – the fact that his father was once beaten up by racists in uniform.

Logan’s is a counter-Abrahamic destiny, sacrificially devoting his life to a reversal of that terrible injustice. This is something more than revenge and more even than forgiveness: a way of showing that black people can be bigger than the bigots, of selflessly transforming his family’s pain into a new future for the police and the community. It’s a trial of strength, both with the racists and with those in his community who think he’s selling out. When his tells his cousin he’s thinking of joining “the force”, the astonished reply comes back: “Like the Jedi or something?” Could this be a playful reference from McQueen and his co-writer Courttia Newland to Boyega’s role in the Star Wars franchise?

Boyega takes his career to the next level with a heroic and even tragic portrayal of Logan. For me, it’s a performance comparable to Al Pacino in Serpico. His Logan is tough, idealistic, self-possessed. He wears the uniform with pride and a hint of self-conscious defiance, carrying off those distinctive copper mannerisms, such as putting on and straightening your helmet after getting out of the squad car.

But everywhere he carries the wound of his relationship with his dad, Kenneth, a first-generation immigrant from Jamaica. Steve Toussaint gives a fierce and passionate performance here as a proud man who has always stood up to police brutality and keeps stern patriarchal standards in the home. There is a great scene when Kenneth is playing Scrabble with the rest of the family and (competitive though he is) misses a chance for major points because the only way would be with a salacious word. Can he ever forgive Leroy for his career decision – and can Leroy ever forgive Kenneth’s non-forgiveness?

The scenes that show Leroy’s life, first in the forensic research labs, then at the police training academy in Hendon, are superbly created in their forthright authenticity, particularly the role-play of how to give evidence in court and how to deal with the defendant in the dock. It’s training that has an ironic resonance with his own dad’s determination to have his day in court. And there’s a great action scene when Logan chases a criminal through a factory – without any help from prejudiced fellow officers who have failed to respond to his call for backup.

Red, White and Blue ends on a note of wintry pragmatism, but not exactly disillusionment. Logan has lived through the reality of racism in the police and has, perhaps, come to terms with the fact that he will never get the simple, clear satisfaction of seeing the racism eradicated or the racists punished. His dad had the same experience with his legal pursuit of the police officers who beat him. The experiences of Logan and Kenneth (and the film only covers Logan’s early career in the police) could be part of a larger historical process whose end they can’t necessarily participate in or even see.

You have to wait until the very end of the credits to savour the full meaning of the title, but the question of patriotism is important. In more than one training scene, Leroy notices a portrait of the young Queen on the wall, a rather poignant, unworldly image of youth and innocence, but also of empire. It is an image that Leroy does not see outside the academy, but that emblem of national unity exerts a distant kind of naive power, considering what Leroy is to experience at the sharp end of police work as he is imposing the authority of the state. Boyega carries the film with a compelling authority of his own.

• Red, White and Blue screened at the New York film festival, and goes on BBC One later this year as part of Steve McQueen’s Small Axe collection.