The growth has been impressive: only 20 months earlier it was on five million downloads. Their biggest market? The US (18.3 million of those 50 million), followed by the UK (3.7 million). In late 2013, Toca Boca reached 50 million downloads at Apple's App Store. In the past three years it has built a significant market share, going up against much bigger hitters such as Angry Birds and Disney. The company was founded in autumn 2010 and released its first two apps in early 2011.

The one app brand I can't find anything wrong with is also the one I understand the least: Toca Boca.

I have reservations about all these sites – but not enough to ban them. We have been through the Club Penguin phase, the Moshi Monsters phase, and we are in the midst of the Minecraft phase. I monitor screentime with my three children (Jack, Vera and Will, 10) where possible. Still, I can understand why you might worry about these things. There is no predator on the other side of the cat's face. Talking Angela is a relative of Talking Tom, the animated cat who is another favourite in our house. Toca Boca's colourful, psychedelic graphics are not a million miles away from the design of Talking Angela, the app that fell victim to a Facebook hoax in February that paedophiles were scripting the creature's questions. It's difficult to know as a parent what's helpful and what's harmful. Vera pipes up: ' Candy Crush is fun!' Me: 'When have you ever played Candy Crush?' (I have never played it and don't have it on my phone.) 'On Auntie Trudy's phone.' (That's my sister.) She turns back to the sloth. But then you look at the app store and think: 'How is it addressing these types of play?' Everything in the app store is in the last category – games and books. 'Most children like all five types of play. Toca Boca divides children's activities into five categories: active play (sport), make-believe, manipulative play (building stuff), creative play (drawing) and learning play (books and games). Jeffery explains that it is just supposed to be fun.

Is there something I'm not getting? The company headquarters in Sweden should have the answer. In a world where everyone is worried about shoot 'em up games and stranger danger, these cartoon cakes, robot nurses and smiley butterflies seem innocuous. My two youngest children, Vera and Jack, three, are captivated by the games. Toca Tailor Fairy Tales: a dress up game.

Toca boca toca boca