When thinking about Brian Cox, it’s hard not to call up the two-word Anglo-Saxon phrase he so punctually spouts on HBO’s “Succession.” (The second word is “off.”) Hard, too, not to hear that phrase rumbling beneath the lines of Cox’s piquant, digressive memoir, “Putting the Rabbit in the Hat,” which tracks his journey from embattled working-class lad in Dundee, Scotland, to, at age 75, improbable pop-culture icon — and which forfeits none of the spiky candor that got him there.

Cox is the product of a dislocated clan of mixed Irish and Scottish ancestry, “besieged by the forces of tribalism and the Catholic faith.” The sudden death of his father, a grocer, when Cox was 8 set his family on “the mouse-wheel of poverty.” With a mother who was both mentally ill and regularly absent, Cox ended up bouncing between relations, an underfed latchkey kid with no stable home life.

His escape was the cinema, and his epiphany a 1960 drama called “Saturday Night and Sunday Morning.” “I looked at Albert Finney, who was working-class English, in a film that wasn’t all about the lives of posh folks in drawing rooms, or struggling nobly in far-off places, or having faintly amusing high-jinks on hospital wards; it was all about working-class people — people like us.”

In that moment came his calling, as unexpected for “a flabby, pimply youth in unwashed clothes” as it was unwavering. “I don’t believe that you have to live through tragedy in order to portray it, but it does help clarify things for you, and for me it all added up to what felt like a formidable singleness of purpose,” he explains. “That was my superpower. It set me on my path.”

He took a jack-of-all-trades job at the Dundee Repertory Theatre, then a slot at the London Academy of Music and Dramatic Art. Welding his proletarian energy to classical training, he staked out a claim as one of English theater’s most in-demand leading men, scoring particular triumphs as Macbeth and Titus Andronicus (and getting felt up, he says, by the likes of Princess Margaret). There he might have remained, quietly totting up his honors and curtain calls, but in the mid-1980s, he set his sights on Hollywood.

Cox had no illusions. He knew that, in a world of big budgets, he could survive only in supporting roles, and that was fine. “What I was influenced by were the wonderful character actors from the 1930s and 1940s. The ones who had a way of creating an arc for themselves, no matter how big or small their role.” To see that process in action, check out Michael Mann’s “Manhunter” (1986), where Cox has just a few minutes of screen time to put across a serial killer named Hannibal Lecter (or Lecktor, as it was then spelled). This isn’t the bulging-eyed psychopath later immortalized by Anthony Hopkins but a calmly inflected, almost banal fellow with insanity tucked lightly up his sleeve. Indeed, if there’s any thread that ties together Cox’s crowded oeuvre — more than 230 acting credits, ranging from Trotsky to Churchill to Agamemnon — it’s that sense of a secret knowledge, a barely cloaked aggression, thrumming beneath his roughened skin.

No wonder the producers of “Succession” tapped him for their antihero, Logan Roy, a right-wing media mogul who refuses the King Lear role assigned to him and spins like a dime between rageful silence and rageful noise. Cox admits that “it can be almost distressingly easy to put on my Logan Roy skin,” in part because “we’re both disappointed in how the human experiment has turned out. We share a certain disgust.”

And, like Logan, he doesn’t mind venting a bit. Quentin Tarantino: “Plot mechanics in place of depth. Style where there should be substance.” Steven Seagal: “Suffers from that Donald Trump syndrome of thinking himself far more capable and talented than he actually is.” Ian McKellen: “A master at what I’d call ‘front-foot’ acting.” Michael Caine: “Being an institution will always beat having range.” Johnny Depp: “So overblown, so overrated.” Cox has little use for Method excess (though he’s forbearing with the self-flagellations of Jeremy Strong, who plays one of his sons on “Succession”), and don’t get him started on directors with their useless notes or actors who decide to rewrite their lines (we see you, Edward Norton). Or actors in general, who are “whores for praise, locked into approbation, capable of killing our offspring in return for validation and living only for applause, both literally and figuratively.”

Cox very much includes himself in that description and cops as well to being an unfaithful husband, a “fairly crappy father” and “a little bit of a diva.” Perhaps it is this substrate of self-knowledge that most clearly separates him from the deeply unintrospective fellow he inhabits on HBO. Well, that and his New York state medical marijuana card and the unstinting devotion to his own craft.

“It really is about reflecting back to people how we are. The great writers do that, and the actors who serve it don’t get in the way. … It’s not a case of ‘I’ll show you this,’ rather it’s a case of ‘I’ll share this with you.' ”

Louis Bayard is the author of “Courting Mr. Lincoln” and “The Pale Blue Eye.”

PUTTING THE RABBIT IN THE HAT: A Memoir

By Brian Cox

Grand Central. 384 pp. $29