This sequel to the first gnome-based animated picture, 2011’s mediocre “Gnomeo and Juliet,” begins with a debate about what story it should tell. One suggestion is “Game of Gnomes,” but the punning options land on “Sherlock Gnomes” instead. Presumably the choice was made on the basis of what happens to be in the public domain.

Whatever the rationale, the movie turns out to be a pretty anemic idea, connected to its predecessor only by the most tenuous of links. Boring Gnomeo (James McAvoy) and feisty Juliet (Emily Blunt) are now a couple, moved along with all their gnome friends and family to a new garden in London. No sooner do they arrive than a wave of disappearances of gnomes breaks out all over the city. Sherlock Gnomes (Johnny Depp), the sworn defender of gnomes, and his partner Watson (Chiwetel Ejiofor) would ordinarily suspect their nemesis Moriarity (Jamie Demetriou), an evil plastic spokesthing for a pie-selling outfit, but he supposedly died during the team’s latest gnome-rescue.

The two teams meet when Gnomeo and Juliet’s garden-mates all vanish while they’re out on the town, and Gnomes and Watson turn up to investigate. Joining forces, after a fashion, they follow the series of clues that arrogant Sherlock works out in a number of surrealistic black-and-white montages, and eventually track the missing gnomes via visits to first a Chinese restaurant and a doll museum, and then to some London landmarks—the Museum of Natural History and Tower Bridge. (“Paddington 2” also used London locations as touchstone places, but did so much more cleverly.) The abductors are revealed to be a couple of gargoyles, but they’re in the employ, as it turns out, of not one but two villains. Their identities are not surprising.

The pursuit has a subtext in Gnomeo’s recognition of Juliet’s strength and her coming to accept his needs too. Meanwhile Gnomes must accept Watson as a friend as well as a true collaborator.

All of this is rather tedious, though the computer animation is good and the 3D effective, though the voice work by the leads and such stalwarts as Michael Caine, Maggie Smith and Julie Walters in supporting roles is surprisingly bland. (The exception is Demetriou, who is so frantic that he quickly becomes grating.)

But there are oddities throughout. A scampering horde of rats in a sewer is likely to disgust parents and kids alike. The Chinese restaurant sequence is loaded with old-fashioned ethnic stereotypes. And for a movie aimed at tykes, including a couple of subtitled sequences makes little sense, since a large segment of the audience can’t yet read.

Then there’s a truly weird sequence featuring Mary J. Blige as Irene, the queen of the doll shop, who sings a new song called “Stronger Than I Ever Was” by Elton John, who’s executive producer on the movie. It’s meant as an anthem to strong womanhood (a topic Irene also discusses briefly with Juliet), but it’s presented in the form of a Las Vegas casino number, and you have to wonder what kids will make of it. Their parents might find their eyes widening, too.

Frankly “Sherlock Gnomes” might have worked better if Gnomeo and Juliet had been excised from the story (along with their garden comrades). One shudders to think what their roles might be in sequels like “Gnome on the Range” and other punning titles.

Of course, stopping the series right now could bring everyone a sigh of relief. Can Mr. John be persuaded? By low grosses, most assuredly, and that’s the likeliest outcome.