Some of the satiric potential in an adaptation of Paul Torday’s book can be glimpsed in Lasse Hallstrom’s “Salmon Fishing in the Yemen.” Whenever Kristin Scott Thomas swoops into the story as Patricia Maxwell, a political advisor to the British ruling party who runs a close second to Meryl Streep’s Margaret Thatcher in terms of fierce determination, the picture takes off into the stratosphere. Unfortunately, Maxwell is a peripheral character, and apart from her, Hallstrom’s film is a bland but likable romantic comedy that gets by mostly on the charm of its leads.

The central figures in the story are Harriet Chetwode-Talbot (Emily Blunt), a PR executive, and Dr. Alfred Jones (Ewan McGregor), a government fisheries expert. Her firm has been hired by a wealthy Yemeni sheik (Amr Waked) to assist him to implement a plan to introduce salmon fly-fishing, which he enjoys in Scotland, to an arid area of his homeland, which he’s turning into a river via a huge dam. Harriet seeks help from the British government, and though Jones dismisses the idea as absurd, Maxwell leaps at it as a means of showcasing frazzled English-Arab relations.

Of course, problems abound, particularly when fishermen protest the notion of stocking the Yemeni location with salmon brought from Great Britain. In Yemen, a group of anti-western locals plot to undermine the project, using violence if necessary. And Harriet and Alfred are gradually attracted to each other, despite the fact that he’s married to a woman as professionally accomplished as he is (Rachael Sterling), while she’s involved with a special forces soldier (Tom Mison) who goes missing while deployed on a dangerous mission.

The advertising woman and the scientist, you will not be surprised to learn, will ultimately come hesitantly together, and you won’t be displeased that they do, since they make such an agreeable—and obviously well suited—pair. McGregor, sporting a Scottish accent and glasses that might remind you of Cary Grant’s in “Bringing Up Baby,” is at his most diffidently endearing, and Blunt cuts a striking figure, particularly in the sequence when Harriet and Jones visit the sheik’s Scottish castle to confer with him about his plan.

So as a low-key romantic comedy “Salmon Fishing” is satisfying enough, benefiting from the stars’ charisma and Hallstrom’s easygoing direction. But Scott’s performance reminds us of how much sharper the film could have been. Certainly more could have been made of the figure of the sheik, who’s portrayed in such fulsome terms that he comes off as a near-saint. At the end, he even seems ready to forgive and forget the terrorists who have blown up his dam, even though their act appears to have cost some lives. Talk about enlightenment!

In all this one can sense the hand of Hallstrom, whose specialty has always involved transforming potentially challenging material into something more viewer-friendly. He and Beaufoy certainly defang what might have been an edgy commentary on bureaucratic buffoonery.

Still, one can’t deny that McGregor and Blunt make an attractive couple, and like all Hallstrom’s films, “Salmon Fishing” is nicely mounted, with lovely cinematography from Terry Stacey and a resolutely pleasant score by Dario Marianelli.

But it’s only when Thomas blazes onto the screen—and, to a far lesser degree, Conleth Hill as Jones’s self-serving boss—that the movie really fulfills its promise.