An actual case of a British whistleblower prosecuted under the UK’s draconian Official Secrets Act is dramatized in Gavin Hood’s docu-drama, which offers an interesting narrative even if the treatment sometimes seems a bit too restrained and discreet for its own good.

Katharine Gun (Keira Knightley) is introduced as a translator working in 2003 at a British intelligence post, GCHQ (Government Communications Headquarters), where her specialty is dealing with Chinese material. But one day a top secret memo lands in her computer in-box that was penned by a fellow named Frank Koza at the United States National Security Agency. At the time the Americans were angling to persuade the government of Labour Prime Minister Tony Blair to join in the invasion of Saddam Hussein’s Iraq, and preparing a campaign at the United Nations to secure a resolution giving the operation international legitimacy.

But some of the current member states on the U.N. Security Council—Angola, Cameroon, Chile, Bulgaria, Pakistan and Guinea—were balking at voting for the resolution, and the memo suggested using wiretaps on their diplomats as a means of gathering embarrassing information to pressure on them to do so; the resolution was especially important for Britain, since it would provide Blair—some of whose officials were dubious about the invasion—with the political cover he needed to join in the operation as part of the UK’s “special relationship” with the U.S.

Aghast at the means being employed to justify what she considered an unnecessary and unjust war, Gun decided to copy the memo and, through activist Yvonne Ridley (Hattie Morahan), transmit it to the staff of a newspaper, The Observer, in hopes of its being published in time to prevent the invasion—or at least a UK role in it. And despite the fact that she admittedly failed in that purpose, she ultimately confessed being the leaker, leading to her prosecution.

The first half of the film is devoted to Gun’s dilemma about what to do and her decision to try to make the document public, much to the dismay of her husband Yassar (Adam Bakri), a Kurdish refugee who fled Turkey for asylum in Britain. Hood, who got the adrenaline running in his earlier thriller “Eye in the Sky,” offers a few suspenseful sequences here—one in which nervous Katharine runs off a hard copy of the memo, another of her trembling as she mails it—but he mostly presents things in a relatively low-key style.

Much of this portion of the picture, moreover, is devoted to work on the part of The Observer’s staff—editor Roger Alton (Conleth Hill), reporter Martin Bright (Matt Smith), war correspondent Peter Beaumont (Matthew Goode) and pugnacious Washington reporter Ed Vulliamy (Rhys Ifans)—to verify the story and the memo’s legitimacy. Finally, despite misgivings—based partially on the fact that the paper had previously editorialized in favor of the invasion—they published, though a mistake in the use of something as ordinary as spellcheck (which turns American spelling into English usage) threatens to undermine acceptance of the scoop.

Gun’s decision to accept responsibility for the leak impelled the government’s decision to bring charges against her—and led to Yassar’s deportation. But while her role in the narrative never disappears, the focus really shifts to the efforts of her lawyer Ben Emmerson (Ralph Fiennes) to mount a defense to the charges. He eventually decides to turn the tables on the government, unearthing evidence that members in the UK administration opined that the country’s participation in the invasion would be illegal in the absence of a proper U.N. resolution. The threatened release of evidence to that effect persuaded the government to drop the charges, and Gun went free.

Here, too, Hood treats the action with a mood of mournful resignation over the Blair administration’s casual cruelty and political duplicity, rather than seething anger (although casting the menacing-looking Peter Guinness as Gun’s chief government tormentor is rather a blunt instrument). It culminates in a scene of quiet sadness on a beach between Emmerson and the government’s chief prosecutor, a friend who effectively admits that he was just following orders.

“Official Secrets” frankly lacks the tension of other thrillers of its type, largely because of Hood’s understated style and the mostly similar performances (apart, most notably, from Ifans, who feasts on his Vulliamy’s volatility). But it is well-crafted, with expert production design (Simon Rogers), cinematography (Florian Hoffmeister) and editing (Megan Gill), wittily incorporating archival clips of figures like Blair, George W. Bush and Colin Powell and other political figures into the footage to add historical context.

The result will never challenge a classic like “All the Presidents Men,” but it is a solid, thoughtful treatment of one aspect of U.S. government chicanery, in collaboration with the U.K., to pave the way to the misguided Iraq war, and of one woman’s courageous if unsuccessful effort to derail it.