“Arthur Christmas” is a spirited, comically chaotic and adorably anarchic addition to the world’s over-supply of holiday cartoons. It’s very British, in other words — from its producers (Aardman, the folks who gave us “Wallace & Gromit”) to its voice casting to the slang slung by the assorted Santas in this 3-D computer-animated farce.

“Assorted Santas?” Why, yes. Santas in this version of North Pole Inc. serve for about 70 years and pass the job down to a son. The current Santa (voiced by Jim Broadbent) is a bit dotty, long-in-the-tooth, more of a “figurehead” in the intricate time-traveling incarnation of the family business that his red camouflage-suited son (Hugh Laurie, perfect) has turned it into. He has a huge stealth spaceship sleigh in which armies of technocrat elves and Fed Ex elves organize deliveries, which armies of commando elves make, with Santa showing up to provide that “official” touch on Christmas Eve. Steve is waiting for the old man to retire. He even has the Armani Santa suit all custom made, and a Christmas tree shaped goatee.

But the old man won’t go. Even a disastrous near “wake up” alert (a child wakes up with Santa in her room) isn’t enough to convince him. Even when the organization realizes that out of the billions and billions served, a little girl in Cornwall didn’t get her bike, a resentful Steve only dismisses that as a statistical anomaly, and Santa himself shrugs it off.

“Don’t worry, children are stupid,” one of the elves offers. They won’t realize they didn’t get a visit from Father Christmas.

Arthur, Santa’s klutzy younger son, winningly voiced by James McAvoy, is shocked. Arthur won’t hear of it. And in his ancient grandpa, Grandsanta, played with demonic glee by the great Bill Nighy, he finds a sympathetic ear. The old man wants to get his old sleigh out and make the delivery, with real reindeer.

“They said it’s impossible,” Arthur protests.

“They used to say it was impossible to teach women how to read,” Grandsanta mutters back. “We’ll be back home in the waddle of a reindeer’s buttocks!”

That’s when “Arthur Christmas” takes off — literally. With outmoded technology, a 136-year-old Santa with false teeth, a bad temper and no sense of direction, Arthur’s going to get little Gwen her bike. They encounter a gun nut in Idaho, a fierce chihuahua in Mexico and a marauding pride of lions in Africa, all in an effort to make sure no child is left behind on Christmas.

“It doesn’t matter how Santa’s gift gets there,” Arthur declares, “as long as it does!”

“Arthur Christmas” has many a madcap moment, many of them provided by the super-efficient gift-wrapping elf Bryony, who believes invisible tape can solve any problem — including that marauding pride of lions.

The Aardman animators know a thing or three about sight gags and throw-away lines, and they pile up quickly here. Nighy’s wicked glee in every little bit of slang is hilarious, but the sheer invention is what gets you.

The silly “Arthur Christmas” is a most welcome treat to find stuffed into the cinema’s stockings this holiday season.