In a play or on a movie, nearly everybody who works with Jennifer Ehle says the same thing: She’s one of the greatest, most authentic, least showy actresses alive. If her relative degree of fame in America – medium-ish – puzzles some of her champions, and her face remains more familiar than her name (pronounced EE-lee), so be it.

“In an ideal world, I would work with her on every project I do,” says director Kathryn Bigelow. The Oscar winner for “The Hurt Locker” cast Ehle in a key supporting role of a CIA analyst in “Zero Dark Thirty,” and brought her in for a cameo in Bigelow’s upcoming ’60s drama “Detroit.”

“She’s the actress of her generation,” asserts veteran stage director Jack O’Brien, who staged Tom Stoppard’s “Coast of Utopia” trilogy at Lincoln Center Theater. For that project Ehle won the second of two Tony Awards; the first was another Stoppard play, “The Real Thing,” a transfer from London and her high-profile introduction to Broadway. “I don’t think anyone can touch her. She has the quiet authority that marks a star. She commands the stage, and the screen, without even seeming to acknowledge that she’s being watched.”

In the perplexing editing phase of his virus epidemic thriller “Contagion,” filmed largely in Chicago, director Steven Soderbergh and screenwriter Scott Z. Burns ended up scrapping entire storylines in order to write and shoot additional footage focused on the Centers for Disease Control doctor played by Ehle, the one who ends up saving the world.

“She can do anything,” Soderbergh says of the actress. “She radiates intelligence, and she has the verbal facility to sell some pretty difficult language.” In “Contagion” Ehle’s character rattles off the following sentence, blithely: “I can see some structures on the surface that look like glycoproteins, but there’s nothing morphologically pathognomonic.” How Ehle deploys that one line to A) impart information, B) reveal something of the idiosyncratic character saying it, and C) hand the audience a strangely funny moment may well be the subject of a future graduate thesis project.

In J.T. Rogers’ play “Oslo,” which just won the Tony Award for best play and earned Ehle a best actress nomination, she plays Norwegian diplomat Mona Juul, who, along with her husband (Jefferson Mays), quietly established a back-channel negotiation in the Oslo Peace Accords in the early 1990s between the Palestine Liberation Organization and the State of Israel. It’s a heady play, and Ehle’s a narrator as well as a determinedly recessive character. Someone, in other words, typically not nominated for a Tony.

“She’s a back-foot person, quite low-key,” Ehle told me between a recent matinee and evening “Oslo” double-header, on the Lincoln Center plaza. A theatrical press agent brings sandwiches and coffee. “So my questions (in rehearsal) are: What are this woman’s obstacles to expression? What are the reasons for her restraint? She’s diplomatic by profession and by nature. She’s cautious. It takes a lot for her to speak up, to speak her mind. But in terms of the story, she has to have a level of charisma, a level of attraction, for these people to find her compelling. It’s fun to put somebody like that together.”

Ehle, 47, was born in Winston-Salem, N.C., to a famous English actress mother (Rosemary Harris, 89) and an American novelist (John Ehle, 91). In London, Jennifer dropped out of drama school to take a major, ultimately notorious female lead in the 1992 Channel 4 miniseries adaptation of “The Camomile Lawn,” set in World War II. Her role, the impetuous Calypso, required copious, full-on nudity. The ogling didn’t die down for years. She was 21 at the time. “It never occurred to me,” she told the Sun newspaper in 2013, “that I was too young to deal with it all.”

Her triumph in the role of Elizabeth Bennet opposite Colin Firth (they dated for a year or so) in the 1995 BBC version of “Pride and Prejudice” reset expectations for good. She lived in England until the age of 30; the work came, sometimes more fulfillingly than others.

Then, in 2001, she married an American, writer Michael Ryan, whom she shares a home in Dutchess County, New York, with their two children, George and Talulah.

It’s a determinedly remote part of the world for someone with a film and stage career. Shortly after the birth of their daughter, a couple of things happened. One, she says, was getting cast in the pilot of “Game of Thrones,” as Catelyn Stark. “Talulah was so young,” she recalls, “and I really didn’t want to be working at all at that point, but I needed to.” So she did it, and then took on the role of Geoffrey Rush’s wife in “The King’s Speech.” That was that, she thought.

But “Game of Thrones” got picked up as a series. Ehle panicked; she’d signed an iron-clad three-year contract, and all she wanted to do was be at home, with her newly expanded family.

The producers, as it happened, were exceptionally gracious and let her out.

It was “Contagion,” which came up a little while later, that “changed a lot of things for me,” she says. “I really thought I’d be completely cut out, from day one.” After all, she’d recently been axed from the final cut of “Michael Clayton,” which Soderbergh produced; her scenes as George Clooney’s girlfriend were deemed less than crucial to the storyline.

“It was one of those heartbreaking decisions filmmakers so often have to make,” Soderbegh told me. “I remember thinking: ‘Well, note to myself: Put her in one of your own films.’ ”

He did. The role of Dr. Ally Hextall, CDC wonk and Laurence Fishburne’s right-hand woman, was right up her alley. Nothing flamboyant on the page, but compelling and full of interpretive possibilities. Since she figured she might not make the final cut anyway, on “Contagion” Ehle felt “completely liberated, like I had the freedom to play her a little weird.” As luck had it, the preview cards and audience survey results indicated younger audiences, especially, wanted more science and more Ally, not less. Eager to comply, Soderbergh brought Ehle and her family to Chicago for a week of additional footage, written on the fly, delivered impeccably.

“Whatever her process is,” Soderbergh says, “Jennifer has that British or at least half-British quality of not burdening other people with it. Also, I should mention that if she doesn’t have the best cheekbones in the world, they’re tied for first.” Before I even get the question out, Soderbergh answers: “Faye Dunaway, circa 1974.”

The adjective “luminous” comes up with wearying repetition in Ehle interviews spanning three decades. “She has extraordinary dignity,” director O’Brien says, “and she’s incredibly warm and open. But she lives a very individual, very private life. On film, and on stage, you’re drawn to her. Even when she’s off in the corner you watch her listening.”

The sort of career Ehle is pulling off in America is far easier, geographically, to pull off in England, where actors zip from a West End play to a BBC miniseries to a film project without major time zone disruptions. Last summer she opened the off-Broadway edition of “Oslo” in the smaller Lincoln Center Theater space. When that run closed, in preparation for a transfer to the larger Broadway house, she promoted “A Quiet Passion” at the Toronto International Film Festival. In writer-director Terence Davies’ film, Ehle plays Vinnie, the ebullient sister of poet Emily Dickinson (Cynthia Nixon).

From there, Ehle worked on five films in two months. In Dublin, she co-starred with Mel Gibson and Sean Penn in first-time director Farhad Safinia’s adaptation of the nonfiction best-seller “The Professor and the Madman,” about the birth of and murderous intrigue surrounding the Oxford English Dictionary. While in Dublin, Ehle filmed a small role in “I Kill Giants,” the Zoe Saldana-headlined graphic novel adaptation directed by another first-timer, Anders Walter.

In Manhattan, she shot “Monster,” with Jeffrey Wright and Jennifer Hudson; then a quick day in Boston for Kathryn Bigelow and “Detroit.” Also Ehle squeezed in “The Miseducation of Cameron Post,” for second-time feature filmmaker Desiree Akhavan.

“I hit a vein, a mother lode vein,” she says. The wind whips up on the Lincoln Center plaza. “I guess there’s been a sea change the last couple of years, starting with ‘A Quiet Passion.’ For years I took the smallest, tightest-scheduled jobs I could, to spend the least amount of time away from home. But I’ve started loosening my bonds a little bit. My children are 14 and 8 now, and I suddenly have these opportunities. And maybe as a family that’s of value, too. Children do love to be around grown-ups happily toiling. So I’ve been doing more. I feel fortunate to still be able to get work, and oddly more and better work than I’ve had before. It’s lovely. I’m grateful.”

She’s happiest, she says, “when the work isn’t results-oriented. When it’s back to, you know, just putting on a show, figuring out how to tell a good story. It’s easiest to find that in the theater. But I’ve been on a lot of film sets this last year where it feels like that, too.” With a quick gathering up of the sandwich wrappings, Ehle smiles and says it again, for emphasis. “That’s when I’m happiest in my work.”