In the third of The Godfather movies, the aging Michael Corleone is trying to rein in his young nephew Vincent, a hothead who's burning to murder some guy who crossed him. "Never hate your enemies," Michael tells him sagely, "It clouds your judgment."

This philosophy gets put to the test in Criminal Record, an enjoyable new crime series on AppleTV+, about two smart, driven London cops who become archrivals. It stars two of the best British actors on TV: Cush Jumbo, whom you'll know as Lucca Quinn on The Good Wife and The Good Fight, and Peter Capaldi, of Doctor Who and The Thick of It fame. Their characters wage a battle that goes beyond the simply personal to touch on questions about the ethics, and politics, of police work.

Jumbo plays Detective Sergeant June Lenker, a biracial woman in a largely white police station. She overhears an emergency call in which a terrified woman says that her boyfriend bragged about once killing another woman and getting away with it — the wrong man has been imprisoned for the crime. Taking this claim seriously, June checks the records and decides the victim of this injustice is a Black man named Errol Mathis.

Doing her due diligence, she visits the officer who handled the original case a decade ago. That's Capaldi's character, Det. Chief Inspector Daniel Hegarty, a man as self-contained and calculating as June is headlong and passionate. Bridling at her implication that he might've jailed an innocent man, he scoffs at her impulsiveness in reading so much into an anonymous call.

Naturally, the two take an instant dislike to one another, and over the next seven episodes, they wage guerrilla war. Convinced Hegarty is not telling the truth, June secretly throws herself into the Mathis case in ways that violate department protocol; meanwhile Hegarty uses his wiles — and dodgy underlings — to stop her from finding information that will cause him trouble. Knowing she's over-eager, he places snares in her path to discredit her.

Like so many cop shows these days, Criminal Record aspires to being more than an ordinary police procedural. To that end, both of its antagonists must deal with confusing personal lives. While Hegarty wrangles a troubled daughter and reckless cronies, June often feels stranded. At home, she has a nice white husband who doesn't always see his own unconscious biases. At work, she's treated with various degrees of bigotry by old-school white male cops; meanwhile, some fellow Black officers allege June is being favored because of her lighter skin.

Now, I'd like to be able to say that Criminal Record offers the revelatory vividness of acclaimed hits like Happy Valley and Mare of Easttown, but, in fact, the show's creator, Paul Rutman, doesn't dig as deep as he should. He touches on tricky themes, like white supremacist cops, then drops them without fully playing out their implications.

But the show is elevated by its leads. Jumbo is a charismatically sleek actress who's sturdy enough to hold her own with Capaldi, a cagey old scene stealer who revels in the chance to play an unreadable tactician like Hegarty. Where Jumbo's June carries her integrity like a flaming torch, it's less clear what we're to make of the hatchet-faced Hegarty, whose air of poised mastery feels like an attempt to contain chaos. He's the more interesting character because we don't know what makes him tick. Is he corrupt? Is he a racist who treated Mathis unjustly because he's Black? Or could he simply be protecting his reputation for being a great detective?

As usually happens in crime stories, the climax is not wholly satisfying — the twists are too neatly tied. Criminal Record hits its peak in the middle episodes when both June and Hegarty are at their most frazzled and devious. While hatred may indeed cloud a person's judgment, a story is always more fun when its antagonists crackle with genuine dislike.