Last autumn, before she and her husband made it into their current Californian lockdown, Meghan Markle recorded the narration for this lavish new documentary from the Disneynature production unit, streaming on Disney+, her fee being a donation to the Elephants Without Borders conservation charity working in Botswana. The film shows the annual, dramatic migration of an elephant herd across the Kalahari in search of food and drinking water, moving from Botswana’s Okavango Delta in its dry season, heading for the Zambezi and the Victoria Falls: the last being an awe-inspiring phenomenon which Meghan matches with her own spectacular torrents of schmaltz. She takes to Disney-narration like an anthropomorphic duck to water. “For elephants, family is everything! In this tight-knit group, someone always has your back!”

The film is directed by Mark Linfield, Vanessa Berlowitz and Alastair Fothergill, veterans of the BBC Natural History Unit, and they get some great scenes and striking moments, working in the immersive, intimate nature-doc tradition pioneered by David Attenborough. But they are also giving us something in the somewhat silly Disneyfied tradition of The Lion King and The Jungle Book, with a cutesy narrative sneakily fashioned in the edit, and everything but Elton John belting out Circle of Life on the soundtrack. The heroes are the herd’s ageing 40-year-old matriarch Gaia, her younger sister Shani and one adorable little baby elephant: “Meet Jomo!” coos Meghan.

As for the others in the herd, they do not have names, and it takes an effort of will to remember that the main three don’t really have names either, unless you speak elephant. “Jomo” “Shani” and “Gaia” are the exotic human names that the directors have given them. There are some making-of-featurette-style scenes over the closing credits, but we don’t get shots of Mark, Vanessa and Alastair arguing in the production office about appropriate names for two mama elephants and a lovable kid. “Elspeth, Mavis and Brian?” — “Nah, not elemental and African enough.” “Nala, Sarabi and Simba?” — “I think it’s been done.”

And so Gaia, Shani, Jomo and the gang set off on their epic quest, and there are some undoubtedly striking overhead shots of the network of water-holes (some treacherously dry) as they lumberingly schlep across the colossal plain. The herd leader’s instinct-memory for where to go is part of an unbroken chain of knowledge stretching back for millennia, and Linfield occasionally shows this with little subliminal speeded-up sequences showing hallucinatory flashes of desert and sky.

There are some fascinating scenes and set-pieces: especially a little calf having to be rescued from one pool’s churned-up mud, and the elephants getting water by tearing the bark from the Baobab trees. But again and again, Markle is given outrageously unverifiable things to say, such as: “Gaia remembers these birds leading her mother to the water….” And Shani later supposedly “…looks back on all the lessons she learned from Gaia.” You expect that this film, like an episode of The Office or Parks and Recreation, is suddenly going to include a shot of Gaia telling on off-camera interviewer: “Mmm, yeah, I totally remember my mom being led by those birds over to this water…”

Once the target has been achieved, a dry season rolls around, and the elephants must turn around and head home. All the while, they are concerned about meanie carnivore-predators, such as the crocodiles who hang out in precisely those shallow waters where elephants like drinking, and of course lions, whose Disney-royal glamour status this film warily concedes. It’s a technically impressive work with some lovely images — and a bit of a sugary taste.

•Elephant is released on Disney+ on 3 April.