Give HBO’s latest drama six hours of your time, and it’ll tell you the story of the 21st century.

That’s the promise made by “Years and Years,” which airs on the cabler starting June 24 after a run on BBC One in the United Kingdom. The first episode begins in May 2019, and subsequent installments push deep into the 2020s, far enough to reveal that our future history looks less like an arc towards progress than a whirlpool of entropy. And though Emma Thompson steals scenes as an ambitious nationalist politician whose brashness and ease with the mechanisms of celebrity could generate comparisons to both Brit Boris Johnson or to at least one familiar American figure, it’s not her story. To its credit, “Years and Years” — among the most emotionally involving, and best, series to air so far this year — keeps its aperture narrow even as the world keeps forcing its way in. This is, above all, the story of a family, one whose ordinariness makes them a powerful vehicle for telling the future.

The Lyons family is a relatively close-knit group who tend towards the upper-middle-class; in the absence of their estranged father, eldest brother Stephen (Rory Kinnear), a banker, plays the part of patriarch. Others among this well-drawn group include his wife, Celeste (T’Nia Miller), his brother Daniel (Russell Tovey, as good as he’s been onscreen), and sisters Edith (Jessica Hynes) and Rosie (Ruth Madeley); grandma Muriel (Anne Reid), oblivious to change, sits at the story’s margins as a reminder of an increasingly less recognizable past. Each sibling interfaces with increasing political change in ways that would feel, in normal times, completely quotidian: Daniel works in housing for the government, Edith is a career activist, and Rosie, who has spina bifida and is a single parent, works in a school. Stephen seems to think about politics little, if at all.

But politics have an inelegant way of clomping into the forefront of lives, at least in this moment and the moments “Years and Years” predicts ahead. Daniel, married and stable, falls in love with a Ukrainian refugee fleeing homophobic torture; Edith, protesting at an artificial island constructed by the Chinese, is caught in a nuclear strike that threatens to significantly shorten her lifespan. Rosie finds herself caught up in the burn-it-all-down rhetoric of Vivienne Rook (Thompson), a person we see in the first four episodes only as a figure covered by the media, one whose appealing lack of an inner life leaves her all image and rhetoric and soothing noise. And Stephen and Celeste face down, first, their daughter’s desire to become “transhuman,” merging her physical form with technology, and then economic vicissitudes that shatter their steady lives and reveal elements of distrust and contempt amid the wreckage.

Nearly every element, here, is conveyed with verve and imagination; though “Years and Years” isn’t sci-fi, for instance, the particulars of young Bethany (Lydia West) becoming a piece of living tech made my skin crawl with their viscerality. Rook, the politician, is played by Thompson with a grim and clipped Northern English accent and with an ebullient willingness to say whatever will keep the camera light on. Thompson nails the way her ilk of politicians are not kind but are endlessly compelling and even in a way funny on-camera, so willing are they to chuck the basic premises by which we live our lives. Both Daniel’s romance and elements of Stephen and Celeste’s marriage fall into cliche (Daniel’s unfortunate beloved Viktor, played by Maxim Baldry, may be the longest-suffering man on the planet by the end of the run), but tend to right themselves through moments that give us the characters and not just the situation. A scene of mass terror involving Daniel and Viktor deep in the show’s run gains its power, for instance, by the fear on the normally hopeful Daniel’s face, his all-at-once realization that the world really is out to get him, or that he wasn’t meant for these times. Writing for the character and performance get us there, even as a lesser show would have just used the shock of dystopian horror.

And Russell T. Davies’s writing here is consistently elegant and, better, resonant. The key question of our times, one so massive that it demands to be broken up into several smaller ones, is how the individual should or even can react to living through increasingly rapid change. TV has made a couple of previous attempts at it: There’s “Westworld” on HBO, which operates in the realm of allegory to illuminate just how surreal we become even to ourselves as familiar reality slips away. And “Black Mirror” has for years now crafted stories in which protagonists face down technological change that has the capacity either to illuminate familiar traits in us, or to break us apart in the process of changing us.

“Years and Years” does something different, something that it feels not illegitimate to rank against the work done by novels. That cross-media comparison has been overused for years now, but watching “Years and Years,” I was reminded not of other shows on the air but of recent novels by Rachel Cusk, Olivia Laing, John Lanchester, David Mitchell, and Ali Smith, all of which framed the journey from our time into the future the way it actually exists for normal, unspecial characters, as a continuous and seamless present in which even unimaginable chaos must be borne up under, given the nature of the alternative.

All of these books are worth citing, together, because they share a crucial trait: Their authors, like “Years and Years” creator Davies, are British. (So, for that matter, are “Black Mirror” creator Charlie Brooker and “Westworld” co-creator Jonathan Nolan.) Britons live in the memory of what had once been; they are citizens of a power that exists now in memory and ritual but no longer as the defining force on the world stage. Little wonder that they are quite so good at telling stories that depict shifts in historical currents not as apocalypses demanding the rise of heroes but as rising tides that, given their intractable power, must simply be endured. Most character’s journeys, here, bring them closer each day to hell on earth (Rosie, oddly enough, is living it up, a Rook supporter vindicated at every turn); all of them convey through unadorned and powerful acting the cumulative exhaustion of living through history without a showy awareness that that is indeed what’s going on. After all, for these unfortunate people, like the rest of us, it is not history they’re living, but simply life.

In our world, Brexit threatens to accelerate the pace of isolation and change in the U.K.; in the world “Years and Years” depicts, that acceleration is helped on by Rook and by global financial chaos, leading to a nation of fearful, suspicious people struggling to get by and to retain the states of mind they’d had before the world collapsed. But what the show does best is depict that which doesn’t change; even after nuclear aggression and the embrace of far-right nationalism and the seeming fall of Europe, the Lyonses still gather for birthdays and celebrations. This isn’t meant to be warming, though, or a “Waltons”-ish message about the power of family even under constrained circumstances. It’s a message conveyed by a show whose brief run hides its major ambitions: The comforts of tradition are all we have to grab onto as the grand narrative of our time plays out. And they may not be enough.

“Years and Years.” HBO. June 24. Six episodes (four screened for review).

Cast: Emma Thompson, Anne Reid, Rory Kinnear, Russell Tovey, Ruth Madeley, Jessica Hynes, T’Nia Miller, Lydia West, Jade Alleyne, Callum Woolford, Jett Moises, Aaron Ansari, Aiden Li, Dino Fetscher, Maxim Baldry

Executive Producers: Nicola Shindler, Michaela Fereday, Russell T. Davies