In “The Birthday Party: A Theatrical Catastrophe,” Ullett, a British-born actor who jokes that he’s so old he actually came to America by boat, spills the beans on the abandoned Geffen Playhouse revival of Harold Pinter’s “The Birthday Party.” The much-anticipated 2014 production was to be directed by Oscar-winninger director William Friedkin, best known for his films “The French Connection” and “The Exorcist” — the latter of which may have inspired some of the malevolent antics Ullett entertainingly chronicles.

This solo show, a Rogue Machine Theatre production directed by Lisa James, is one of those delightful instances of theater thinking outside the box. The hour-long piece is performed at the pocket-sized Henry Murray Stage, an attic-like space laid out like a cozy living room.

Ullett is already in place, leaning on a bar stool, as theatergoers file in. The metaphoric fourth wall is nowhere in sight, as the actor casually banters with audience members. A good many fellow thespians are in attendance. The look of glee on their faces suggests they may have an insatiable appetite for the theatrical equivalent of inside baseball. Or maybe they just appreciate a juicy story well told.

Droll in that articulate British way that never seems to break a sweat, Ullett is an expert raconteur — crisp yet colloquial. His manner is that of a genial dinner party host who has a doozy tale to unfold — one his guests might be more eager to savor than the meal itself.

The cast of this ill-fated Pinter revival was exceptional and overwhelmingly British. Steven Berkoff, Tim Roth and Frances Barber (a London stage veteran whom Ullett compares to Judi Dench) were the big names. Ullett had originally auditioned for the meaty, menacing role of Goldberg, but this part went to Berkoff, a noted playwright as well as an actor with a long track record of playing bad guys.

Directing, as this yarn suggests, is 90 percent type-casting.

Ullett was thrilled when unexpectedly Friedkin offered him the role of Petey. The opportunity to take part in this stellar Los Angeles revival of a modern classic by one of the lions of the British theater seemed almost too good to be true. Sadly, that turned out to be the case.

Fatefully, Ullett volunteered to serve as the Actors’ Equity deputy of the company. It’s a requirement of the union that one of its members be elected representative of the production to keep Equity informed of workplace conditions and disputes. It’s a job that Ullett has performed without incident in the past, but his sangfroid was tested by a battle of colossal egos that could give “Godzilla vs. King Kong” a run for its money.

Friedkin, who receives a hefty share of the blame, had directed a 1968 film version of “The Birthday Party.” According to Ullett, he seemed to think he was directing another movie of the play. His nonchalant attitude toward the exigencies of the stage rankled the more experienced cast members, who resented the way he tried to control their every movement. Dictatorial about the visual scene, he seemed indifferent to other aspects of dramatic storytelling, as the rehearsal clock ticked ominously.

Berkoff, a master of menace, apparently became savagely Pinteresque in the rehearsal room, browbeating members of the collaborative team, railing at what he took to be American cluelessness and rolling his eyes at the general obsequiousness toward Pinter, a fellow playwright he appeared not to hold in all that high regard. But it was Friedkin’s combination of Hollywood swagger and theatrical bumbling that really seemed to enrage Berkoff most.

Eventually, Berkoff couldn’t stand it any longer and, in a fury hightailed it to LAX in a rental car that bore the dents of his anger, leaving the production without a Goldberg. Ullett quips that it was as if this revival of Pinter had been suddenly rewritten by Samuel Beckett. The new play, “Waiting for Goldberg,” was (in Godot-esque fashion) never going to arrive.

Friedkin had demanded that another British actor of Berkoff’s stature be found. That there were scores of capable actors within a five mile radius of the Geffen Playhouse (Ullett among them) hardly mattered. Practicality was not how Friedkin operated. As the search disastrously proceeded, he burned through money on the production as though Paramount Pictures were footing the bill.

A life in the theater will break your heart. But first it will attempt to make you crazy. As “The Birthday Party” fell apart, Ullett was contending with other professional disappointments. His guest appearance on a popular sitcom ended on the cutting room floor. Adding salt to his wounds, his hope of getting cast as the understudy in the West End production of “Bakersfield Mist,” the play he starred in with his wife, Jenny O’Hara, in the world premiere production at the Fountain Theatre, came to naught.

But no experience is wasted for an artist. And the “catastrophe” of this not-to-be Pinter revival has yielded anecdotal treasure. Names sometimes escape Ullett, and details of his story aren’t always properly set up. But he has a talent to dryly amuse. What’s more, his incisive candor elevates theatrical gossip into something more enriching.

O’Hara warned her husband that if he tells this story onstage he’ll never work in this town again. Fortunately for us, he didn’t listen.

In a talk-back at the end of the show, Ullett admitted that he quite liked Berkoff, ornery though he was, and that he respected Friedkin’s stature as one of the great film directors. Randall Arney, the Geffen Playhouse’s artistic director at the time, comes in for some criticism — confirming my original take on the situation. But there’s no score-settling malice here. Underlying this anatomy of a train wreck is a thespian’s indestructible love of the madness of theater.