It’s a potent moment for a film like “Words of War,” as press freedoms and other accoutrements of democracy seem to be under attack around the world. There remain few stronger recent-history illustrations of that threat than the case of Anna Politkovskaya, a prominent Russian journalist noted for her relentless exposure of government corruption and harmful policies, particularly around the Second Chechen War. Presumably in retaliation, she was assassinated two decades ago — on Vladimir Putin’s birthday, yet.

Politkovskaya certainly merits the admiring dramatic treatment accorded by “Words of War,” which counts Sean Penn among its executive producers. But this U.K. production, with Maxine Peake in the central role, earns more points for its noble intentions than artistic inspiration or raw impact. It’s a polished, pedestrian biopic, with direction by British TV veteran James Strong that smooths over instead of elevating Eric Poppen’s cliche-riddled script. While the subject matter is compelling,...