There’s definitely a British—and particularly Aardmanesque—vibe to this new film from the Laika studio—and not simply because, as is usual with their work, the animation is old-school, in their case beautifully realized stop-motion work (stay for the credits to see one scene being literally built for the cameras), but because the humor is more understated and eccentric than is customary in what passes for what is euphemistically called a “family movie” as made by other American studios, which is ordinarily just a synonym for a picture that’s loud and coarse.

On the other hand, “Missing Link,” written and directed by Chris Butler, who previously helmed “ParaNorman” and penned “Kubo and the Two Strings,” is based on a premise that has begun to grow musty in the overstuffed animated world—the discovery of a “legendary” species. Not long ago “Smallfoot” told of an encounter between man and yeti (as apparently the upcoming “Abominable” will, too). “Missing Link” starts with a prologue about “finding” the Loch Ness monster, but mostly concerns the unveiling of Sasquatch.

The “discover” is Sir Lionel Frost (voiced by Hugh Jackman), an intrepid but self-absorbed Victorian explorer obsessed with making a find that will ensure his acceptance into the prestigious Optimates Society headed by snooty Lord Piggot-Dunceby (Stephen Fry). After his attempt to photograph Nessie goes awry, leading his assistant Lint (David Walliams) to quit, Frost receives a letter from someone in America inviting him to Washington state, where Sasquatch awaits. Piggot-Dunceby, afraid that such a discovery would force him to accept Frost into the society, hires snarky thug Willard Stenk (Timothy Olyphant) to see that he doesn’t succeed.

In America, Frost finds that Bigfoot (Zach Galifianakis), a sweet, modest creature who converses with him amiably and whose only real flaw seems to be that he takes everything too literally, wrote the letter himself. He’s lonely and hopes that Frost will help him find others like him whom he can live with. In return for providing proof of his existence to take to the society, Bigfoot persuades Frost to take him to the Himalayas, where his apparent cousins, the yeti, live in a secret location that Fortnight, a now-deceased explorer, had called Shangri -La.

Accosted and then pursued by Stenk, Frost and Bigfoot proceed to the mansion of Adelina (Zoe Saldana), Fortnight’s widow (and an old flame of Frost’s), to secure her late husband’s map to the place. After much comic business, Adelina insists on joining the expedition, and the trio soon arrive in the Himalayas, pursued now not only by Stenk but by Piggot-Dunceby himself. After making contact with elderly guide Gamu (Ching Valdez-Aran) and her granddaughter Ama (Amrita Acharoa), they find their way to Shangri-La, where the yeti reside under the rule of an imperious elder (Emma Thompson). But their welcome is not all they’d hoped for, and their pursuers are not far behind.

There are action sequences in “Missing Link,” and they’re done with visual exuberance and a nice sense of humor. But they’re less raucous than what you’d encounter in most animated fare, and in any event the film concentrates on quieter moments of goofy conversation and physical comedy that recall the old Hollywood more than the new. The movie coasts along agreeably, offering old-fashioned slapstick and geniality in contrast to the overbearing noise and clutter of most of today’s animated family fare. What stands out in narrative terms is the quirkiness and whimsicality of Butler’s script and staging; the result might be too subdued for small children brought up on today’s animated mayhem, but older viewers will be more attuned to its relative restraint.

The cast pitch their performances accordingly. Saldana is a typical spitfire and Fry the epitome of pompousness, but Jackman avoids going overboard with the haughtiness, and Galifianakis makes Bigfoot, who chooses an unusual name for himself, a gentle, articulate soul who lets out a roar only rarely. Olyphant brings an appropriate oiliness to the villainous Stenk and Thompson a nasty edge to every word that drips from the mouth of the Yeti Elder.

In the end, though, for all the charm of the story and characters, what’s truly memorable are the visuals, every frame a work of art, courtesy of production designer Nelson Lowry, costume designer Deborah Cook and the army of animators working behind the scenes to create the stop-motion effects. Stephen Perkins’ editing is trim but unhurried, and Carter Burwell’s score avoids bombast, adding to the film’s cultivated air.

“Missing Link” is unlikely to achieve the sort of blockbuster status that Disney-Pixar product does. But its jewel-like technical precision will add to Laika’s reputation among animation enthusiasts, who should also appreciate its more subtle, off-kilter narrative approach.