Wood is a firm believer in taking material out to children and watching how they respond, so perhaps it’s no surprise: “Very often, a good response is when they say nothing, and they are absolutely absorbed. But the most important response is do they smile – because that always signifies understanding.”

She cites the start of the show, where a boat goes out of frame, then comes back in, then goes out of frame again. “That sequence is virtually playing a peekaboo game with a very young child: Where’s the boat gone? Here it is, coming back again.” A recent survey found that a game of peekaboo is the surest way to make a baby laugh.

Often, her programmes are designed as a conversation between the television and the children watching it. “When people objected to Teletubbies, we used to say: ‘Look, Teletubbies understand babies, and babies understand Teletubbies. If you’re watching Teletubbies without a child, you are only getting one half of the conversation.’”

Although children live in the same world as us, they perceive it differently. A little girl with a baby brother might posit that all babies are born boys, and then turn into girls, for instance. Or that houses fall down to Earth and then walk into position, using their legs. “You can see how young children will often say things that we think are funny because their perception is that X is the case, when in fact Y is the case. That difference needs to be respected, but equally it can be the stuff of content,” says Wood.

For Wood, the design of shows like Teletubbies is intuition combined with years of trial and error. “I think the only skill I have, if I have one, is being able to watch a screen like a three-year-old might. It is about knowing when to pause, how long to pause for, how to make that comic, how to use anticipation.”

Some adults, however, didn’t get it. The show was accused of “dumbing down” children’s TV and criticised for its constant repetition, poor plots and lack of sense of place. But that was exactly the point. Teletubbies was perhaps the first TV show specifically designed for one-to-two-year-olds. One Norwegian TV executive has described it as “the most market-oriented children’s programme I’ve ever seen”.

“For me, Teletubbies is entirely around that early stage of life when the child is coming to grips with their own body and their own physicality: walking, talking, running, falling over – all of the things that the Teletubbies did,” says Davenport. The green-hilled set was designed to accentuate the depth of the physical space they inhabited, and much of the show simply involved the Teletubbies coming and going and popping up and down, playing with those physical concepts.

The Teletubbies were conceived as technological babies, set in a technological superdome. Even the windmill on the hill is a nod to one of the first pieces of technology children encounter: a pinwheel on their pram. Their bodies were painted bright fluorescent colours, because that seemed to fit with the technology theme, as did putting the TV screens on their stomachs – TVs that showed videos of children doing simple activities out in the real world.

1997’s Teletubbies was the TV equivalent of a Hollywood blockbuster, going on to air in over 120 territories in 45 different languages. Tinky Winky, Dipsy, Laa-Laa and Po were inspired by a trip to the Smithsonian Institution in Washington with Anne Wood, founder and creative director at Ragdoll. They wandered into an exhibition about space and Davenport said, “Isn’t it weird how they put all this technology into the spacesuits, and when you see them walking about in them, they look as much like babies in nappies as anything.”

Upon graduating, he and a friend set up a theatre production company, and it was through this that he landed a job as a writer and puppeteer on a Ragdoll Productions show called Tots TV. The show, which featured three ragdoll friends, their pet donkey and a mischievous dog, won two BAFTA awards, finding audiences in the UK, US, Central and South America. But it was nothing compared to what Davenport did next.

© Andrea D’Aquino for Mosaic

After the success of Teletubbies, Davenport and Wood moved on to In the Night Garden, which Davenport describes as a “contemporary nursery rhyme” aimed at two-to-three-year-olds. “It’s that stage where the child has come to grips with the physicality of the world and is now fascinated with the idea of turning what it knows on its head in an abstract way – the time when nursery rhymes, language play, symbolic play, toy play start to become the thing.” Each character is designed to stand alone, just like Humpty Dumpty or The Old Woman Who Lived in a Shoe do in a book of nursery rhymes.

The central character, Iggle Piggle, represents a kind of ‘every-child’, who lollops around trying to make sense of it all. Davenport says he was inspired by a little girl who used to say “Iggle Piggle Iggle Piggle Iggle Piggle” whenever she was excited. There’s also Makka Pakka, a beige, round-bodied creature, with a penchant for collecting piles of rocks and washing things with a sponge – his face, Iggle Piggle’s face, his rocks, his scooter…

Davenport is fascinated by the idea of accessing his audience through their own preoccupations and interests. Rock-collecting was a childhood hobby of his, while the obsessive washing is not about cleanliness but engaging with an activity that many young children find challenging: washing their faces and getting ready for bed. “The idea is that you can create these little nuggets of action, routine, rhyme or song which become something that parents and children can share together to get through something that might be tricky or difficult,” he explains.

I remember In the Night Garden’s opening sequence – which involves a rhyme about a little boat no bigger than your hand circling round and around in the ocean, while an adult traces circles on a child’s palm. It was a failsafe way to put my son to sleep. When I tell him, Davenport sounds genuinely moved. “When these things are working, they do become components of the relationship between the parent and the child”.

Davenport has seen his godson using Makka Pakka’s song as a way to wash his hair and face. “When you find that something is useful, that’s obviously incredibly satisfying and rewarding,” he says.

This is what led him to approach the University of Sheffield during the development of Moon and Me. He’d read a study where two groups of children were taught a lesson including either standard materials or some involving the Teletubbies. Those working with the Teletubbies material seemed far more engaged than in their normal lessons – in one case a child who barely spoke and hardly took part in class activities returned their completed task asking for another one.

“If you approach children through their own culture, rather than imposing your culture on them, they are much more motivated and more interested,” says Davenport.

Moon and Me is aimed at a broader age range than either Teletubbies or Night Garden. It’s a tale about a toy house coming to life at night, of the sort that were popular in the 1940s and 50s. Having read about the work with Teletubbies, and becoming intrigued by the idea of child culture, he approached the researchers about doing a study to learn more about how contemporary children play with toy houses. The result was his collaboration with Dylan Yamada-Rice, now at the Royal College of Art in London.

“There is still a general assumption that stuff can be made for adults and just dumbed down for kids without looking specifically at the needs of that young audience,” she says. But if you want them to learn anything from it, you need to find ways of engaging that young audience.

“If you can’t believe in the depth of the character and that one character deeply cares about another character, then you’re not going to be very effective in maintaining children’s interest. And if you don’t believe in that character, then you’re not going to care that they are writing a letter to the moon.”

Yamada-Rice joined together two large toy houses from the department store John Lewis, and fitted them with tiny cameras, pointed not at the children but at the toys within the houses. They then assembled a group of one-to-five-year-olds from different cultural backgrounds and set them loose on the toys, recording how the toys were moved, what the children were saying as they played with the characters and what voices they were giving them.

One thing they noticed was the children’s preoccupation with transitions: going up and down the stairs; in and out through the front door; into bed for sleep and back out again; and the importance of sitting down for tea. Another observation was how the children often had multiple scenarios occurring on different floors of the houses. “Maintaining them all was a bit like spinning plates,” says Davenport. “So, a shot which recurs a lot in Moon and Me is of the whole house with all three floors exposed, so you can see the characters on the different floors and stairs”.

I sit down with Tim Smith and watch an episode. There’s the narrator tucking the various characters into bed on the different floors of the house. There’s Moon Baby ringing the front doorbell and Pepi Nana letting him in. There’s a shot of Pepi Nana walking down every step of a staircase.

Smith points out the moonlight lighting up Pepi Nana’s face as she sits up in bed; the use of noises, such as Colly Wobble’s tinkling bell, to cue viewers’ attention and prompt them to seek him out; the adult narrator asking “What’s next?” as Mr Onions lays the table, and then a subtle flash of movement near the cups. All of these, he says, help engage the child’s attention and help them to follow the story.

There are subtle lessons woven into the fabric of Moon and Me, such as the art of structuring a letter, and telling a story – core principles of early-years education – or Pepi Nana climbing into a tub, which rolls away, and then popping out of it again, which helps teach about object permanence. Davenport tells me his shows aren’t intended to be “educational”. His audience, he says, is pre-educational. He strives to provide what he describes as “the unfatiguable exercise of mind”.