The Chapman Brothers: Children's Art Commission, Whitechapel Gallery

When Jake and Dinos Chapman first came to the attention of a wider public at the Royal Academy’s Sensation exhibition, their work came with a parental warning: a sign barring under-18s. After all, naked child mannequins sporting surprised-looking anal apertures for mouths and erect penises for noses were not, until then, the Royal Academy’s usual fare.

But the Chapmans, whose works have always delighted in puerile humour, have never been convinced by the notion of childhood innocence. What's more, even at their most macabre and apparently shocking, their imagination has always had associations with childhood: dopey clown faces meticulously painted on to Goya’s victims of war; tiny toy figures committing cannibalism. And all this probably explains why their new series of children’s etchings, commissioned by the Children’s Art Commission, is hardly any different to their “adult” work.

The series draws on the Chapmans' forthcoming children’s book Bedtime Tales for Sleepless Nights, and, as one might expect from the former enfants terribles duo of Britart, it’s a book that subverts the traditional Victorian morality tale. So each beautifully coloured, lovingly produced print in this small exhibition is accompanied by a horrible rhyme: “Sticks and stones/ Shall break thy bones/ And words will surely hurt you/ Eyeballs and teeth/ Shall be wrenched by grief/ As nightfall comes to shroud you.”

This is all fairly typical for the thoroughly modern, post-Roald Dahl child. But amid the wormy eyeballs, the flayed, corrupting flesh and grinning skulls, the Chapmans like to sail closer to the wind. A huge swastika in a desolate landscape resembles a structure that is part big wheel, part gallows, and floppy, faceless, doll-like figures are attached to it by their necks as it creaks round. Elsewhere, a blood-splattered crucifix is festooned with eyeballs crawling with worms. There are skulls and Nazi insignia aplenty.

But as the Chapmans themselves have said, little can surpass the grisly imaginings of children themselves. And don’t children just delight in the things that make their parents uncomfortable? This is, perhaps, the true nature of childhood, and one doesn’t have to delve too far into Freud to work this out: the age-old theme of innocence versus corruption is, after all, the basis for all children’s fairy tales, and so the vile behaviour of wicked-minded adults who endanger the lives of children is a compelling theme for young minds.

In the second gallery, earlier prints accompany the Children’s Commission: black-and-white illustrations from their series Gigantic Fun. The Chapmans have drawn on the pages of children’s colouring-in and join-the-dots books. There are dozens of these stacked high on the walls, with the more explicit images placed above child-height.

But these have evidently not been executed with children specifically in mind, for the interventions include a realistically drawn foetus with an adult penis, drawn beside the join-the-dot depiction of a smiling elephant, its trunk making an obvious sexual association; a hanged man on a gallows, barely discernible behind the head of an innocently grinning child; a dagger, wielded by a Philip Guston-style disembodied hand, penetrating the head of a boy in a paper hat, playing with his own toy sword (pictured right). You have to peer quite closely to discern some of these drawings, but in contrast to the flat outlines of the original illustrations each has been meticulously drawn. It's as if, underneath such saccharine images, the child’s subconscious desires are erupting unbidden.

Adult Chapman fans will surely delight in these prints. And they might even brave bringing their children along.

• Jake and Dinos Chapman: Childrens Art Commission at Whitechapel Gallery until 31 October
• Find Bedtime Tales for Sleepless Nights on Amazon