Worried about suffering withdrawal symptoms from “Slow Horses”? Well, in a shrewd bit of scheduling, just as its fifth series concludes, Apple TV is premiering yet another Mick Herron adaptation centered around the bumbling inner workings of British government, starring an Oscar-winning national treasure to boot.

Commanding center stage in “Down Cemetery Road,” however, is Emma Thompson in a role which, like Gary Oldman’s slovenly antihero, has the potential to define her latter-day career. 

The Dame is, of course, no stranger to the small screen, having earned a BAFTA for ‘80s miniseries “Tutti Frutti” and “Fortunes of War.” And who can forget her Emmy-winning cameo in “Ellen,” triple duties in “Angels in America,” and scarily prescient turn as a right-wing politician in Russell T. Davies’ “Years and Years”?

But this engrossing eight-parter is the first time she’s led a show in the streaming age. And, judging from its first three episodes, she’s immediately struck gold.  

Thompson plays Zoë Boehm, a private investigator every bit as spiky as her pixie cut. Much of her derision is reserved for Joe (Adam Godley), her downtrodden husband and more pragmatic partner-in-crime. “Is it another desperate damsel in search of a knight in shining cardies,” she sneers about his new case, the first of several withering putdowns which instantly establishes who wears the trousers. “Sometimes I feel like your mum, picking you up from the f**k-up creche” is another.  

Art restorer Sarah (Ruth Wilson) also bears the brunt of Zoë’s acidic tongue when she shows up at her unkempt office looking for help. (“Let me guess, you’ve got a husband, he’s got a secretary, am I warm?”) Of course, having just survived a fireball that’s ripped through her suburban neighborhood, it’s arson rather than adultery she needs investigating. Well, that, and the small matter of a conspiracy involving the Ministry of Defense, a neighboring assassin, and a young girl who may or may not be dead.  

Indeed, ever since her painfully middle-class dinner party was interrupted by a nearby house explosion — depicted in the kind of slow-motion you’d expect from a Zack Snyder film — Sarah has become something of an amateur P.I. herself. Unwilling to buy the tragic accident narrative, she makes herself a nuisance at the police station and the hospital, spurred on by a mysterious newspaper photo which appears to have cropped out a child she witnessed being rescued from the scene.

But is all this in the imagination of a bored forty-something looking for distraction from her faltering marriage to a man obsessed about keeping up with the Joneses? Or, as suggested by the shadowy figures appearing to trail her every move, are there really more nefarious things at play? 

Of course, by this point, we already know the answer, confirmed by a series of secretive boardroom meetings between the cartoonishly domineering MoD head known as C (Darren Boyd) and weaselly underling Hamza (Adeel Akhtar). The former also gets his fair share of zingers, continually unleashing his disdain with the potty-mouthed zeal of “The Thick of It” favorite Malcolm Tucker.

“I’d love a heads-up on what Wreck-it-F**king Ralph has got planned for an encore,” he scoffs on learning how a planned hush-hush operation has literally gone up in flames. And it’s safe to say his employee review of “You couldn’t protect him if he used you as a condom,” wouldn’t typically get past HR. It’s a double act which recalls the boss/servant dynamics of British classics like “Blackadder” and “Fawlty Towers.” A spinoff sitcom, should both parties make it to the end with their lives intact, that is, wouldn’t go amiss.  

Screenwriter Morwenna Banks — continuing the “Slow Horses” connection having previously penned four episodes — generously ensures each character is given the chance to shine. Sinead Matthews also provides plenty of comic relief as Wigwam, Sarah’s well-meaning but idealistic hippie neighbor whose domestic bliss unravels in the unlikeliest circumstances. And although fully aware of the personal and professional pecking order, Joe is occasionally allowed to bite back (“Now that Cruella’s gone to hunt for puppies, who’s for a coffee?”).  

Meanwhile, the ever-dependable Wilson, finally sharing the screen with Thompson having shown up separately in “Saving Mr. Banks,” makes Sarah’s outlandish situation feel believably grounded, the fact her valid concerns are routinely shrugged off indicative of a culture all too quick to dismiss the female voice. And while she’s very much the straight guy to Thompson’s livewire, she’s still afforded the opportunity to get her hands dirty, whether setting off fire alarms or wrestling with hired killers in her own immaculately decorated lounge.  

Nevertheless, “Down Cemetery Road” undoubtedly belongs to its biggest star name. Thompson can play the formidable, no-nonsense antiheroine in her sleep, but she’s on especially sparkling form here as a figure with a near-pathological aversion to manners and moral compass that’s dubious at best. She’s undoubtedly less disheveled, and presumably more fragrant, than Oldman’s Jackson Lamb, yet she’s arguably just as flawed, another example of Herron’s ability to make his female characters as complex and three-dimensional as his male.  

And while it’s never in any doubt that Zoë will forge a mismatched buddy duo with Sarah, it’s fun watching make her wait, advising her to scratch her armchair sleuth itch with board games and get back to focusing on her “bland scatter cushions.” Likewise, her sheer disdain for anyone who doesn’t fit her free-spirited mold. “Seriously, this is what you want to do with your life?” she asks an aspiring Twitch streamer who helps her clear up some valuable grainy CCTV. “F**k me.” 

It would certainly be a grave mistake if Apple TV didn’t also adapt the three further follow-up novels putting Zoë on the case. Alongside “Elsbeth,” “High Potential,” and “Poker Face,” “Down Cemetery Road” belongs to that refreshing new club of semi-comedic mysteries giving women the greatest sense of agency. And, in Thompson, it has the most compelling agent.  

“Down Cemetery Road” starts streaming on Apple TV on Wednesday, October 29 with two episodes.