The notion of creating a safe space for an audience to experience a work of theater tends to provoke the tough-guy purists, because it sounds like coddling. Shouldn’t the stage be a place of daring, unhampered by any content revelations that might spoil the surprise?

Presumably, anyone who arrives at St. Ann’s Warehouse in Brooklyn to see “Grenfell: in the words of survivors,” a tense and enthralling documentary play about a 2017 residential fire in West London that killed 72 people, is aware of the potentially upsetting subject matter. But before the storytelling even starts, the actors in this National Theater production set about making a safe space with a preamble whose clear language and kind tone are not the least bit soppy. [...]

Our humanity tended to, the characters begin their recollections — nothing traumatic, not yet, just simple, sun-dappled memories. Because before Grenfell Tower, a 24-story public housing block, became a cautionary tale about the dangers of government penny-pinching and corporate corner-cutting, it was people’s home.

Thinking back on the apartments that had been their sanctuaries, they miss the freedom of life above the tree line, the view of the fireworks on New Year’s Eve, the quiet when they’d shut their door and leave the noise of the city outside. They miss the community of good neighbors. [...]

As the fast-moving fire began consuming the building in the wee hours of June 14, the residents’ sense of their homes as inherently safe spaces was so deep-rooted that it kept many from recognizing the danger. So did the conventional — and in this case, egregiously inapt — guidance from authorities about remaining in place if a fire is not in your apartment.

Sparely staged by Phyllida Lloyd and Anthony Simpson-Pike, and performed by a superlative, much-doubling cast, this play by Gillian Slovo is activist theater. Using interviews with Grenfell residents and testimony from a public inquiry, it makes the case that whether people lived or died that night depended hugely on chance, and on whether and how soon a person’s urge to flee overrode the ingrained habit of obedience to official advice. [...]

The play argues powerfully, and affectingly, that the marginalization of the Grenfell residents — many of them low- and middle-income immigrants and people of color in a plush, trendy London borough — not only played a part in the emergency response to the fire but also created the conditions for such a disaster. [...]

“Grenfell” will teach you about that cladding — there is a diagram, shown on the video screens that hang above the audience — and its red-flagged safety testing. Other renovation details are similarly alarming, like renumbering the floors so that apartment numbers no longer matched them, creating an obstacle for firefighters.

Toggling between these drier, more cerebral sections and the memories of 10 residents — each vivid, eloquent, endearing — the play regulates the production’s anxiety level, keeping it from overwhelming us.

It is remarkable, though, how much suspense is built into the performance, when the title has already told us that all of the people we’re listening to made it out alive. At one particularly fraught point in Act 2, as the fire raged and a few characters had yet to escape down stairwell paths suggested by slender lines of light, I wondered if one of them was going to turn out to be a ghost.

Arriving at the height of the theater season, “Grenfell” is the opposite of razzle-dazzle: serious, respectful, blood-boiling, aggrieved — and, over the course of its three hours, both gripping and important.