Conceived as a utopian city within a city, the labyrinthine London landmark had a troubled path on its way to being hailed as an architectural icon. But is this world-class arts centre now in danger of being turned into a shopping mall?

It looks like something from a wildly imaginative sci-fi comic, an impossible vision of worlds slamming into each other in a fantastical collage. Elevated walkways leap across the sky while a trio of towers rise up like serrated blades, their edges sawing at the clouds. Beneath them, fountains cascade and cafes spill across lush waterside terraces, while an art gallery and library jut out overhead. A tropical conservatory wraps around the top of a subterranean theatre, next to a cinema buried beneath a crescent of apartments. And the entire multilayered edifice floats above a 2,000-seat concert hall carved into the ground.

This is no sci-fi comic, but a cutaway diagram of the Barbican arts centre dating from 1982, rendered in vivid orange, red and green. Somehow, this miraculous Escher-like wonder really did get built, and it hits 40 this month, with celebratory events and a handsome new book modestly titled Building Utopia.