Ernesto Neto, Hayward Gallery, London

It's quite an artwork that can provoke a crisis of identity in a grizzled old critic like me, but that's definitely what is going on here. The question is: which Teletubby am I?

The little red one with the circle on its head or the purple one with the handbag? Then again, there's the green one with the TV screen ... from which you'll gather that I'm on the top floor of the London's Hayward Gallery in an installation by the Brazilian artist Ernesto Neto.

You don't know Neto? This may give you an idea. His latest work – all two large rooms, linking corridor and three terraces' worth – is made out of whatever women's tights are made of. Let's say, sheer nylon.

In previous Netos, he has exploited the stretchiness of this material to play games with gravity. Typically, he has filled dangling nylon sacks with scented things: off the top of my head, I remember camomile and, I think, coffee beans. The result is an endlessly self-reflecting metaphor, the obvious weight of Neto's stalactites equalling the heaviness of their scent and vice versa. If I close my eyes and think of a Neto, what comes to mind are uvulae – big, pendulous, organic things hanging at the back of mouth-like caves. To walk through a Neto is to feel like Raquel Welch in Fantastic Voyage.

Or, now, like La-La, or is it Po? The uvulae are still hanging from the soft palate of Neto's latest work, The Edges of the World, but they are joined by a whole new set of matching membra. My favourite is a green nylon scrim, stretched flat across one side of the room about a foot above the floor. Alarmingly, you are bidden to walk on this – what is the Portuguese for Health and Safety? – which seems vaguely worrisome until you do. The scrim turns out to be all give and no bounce, so that the effect is of walking on a moss-green mist. From distant memory, it is like taking one of the nicer recreational drugs, or happening accidentally upon Teletubbyland.

But, I hear you ask: is it art? It is a truth generally acknowledged that art must not be fun, and The Edges of the World is definitely that. The section in the back room steers you through a suite of multicoloured caves or viscera out on to a terrace where you can plop, turd-like, into a tub of water – an inflatable swimming pool with its own pink crocheted hairnet and matching his 'n' hers yellow changing rooms. (Dips have to be booked on 0844 847 9910.) Crochet comes into its own in Neto's new work, securing the tubes that run between the inner and outer membranes of his caves or, decked with tiny pink or blue ribbons, edging fields of scrim. It lends the faint air of a maiden aunt to the project, an effect heightened by the Lascaux lavender bags stitched into one wall of the tunnel.

And art? Well, yes. My fear for The Edges of the World is that it will be seen by middle-class parents as a bouncy castle made for their children and so be filled with shrieking Toms and Daisys. Actually, it is a playground for adults from which pre-teens should be barred. The point of Neto's work is to rediscover homo ludens (Playing Man) – to get City brokers beating out a kettle-drum pulse in an adult-sized sheer red heart, or overeducated art critics making like Tinky Winky.

To do this, The Edges of the World needs to be grown up, and it is. Neto's genius lies in his understanding of scale and instinct. As you climb the rickety plywood stairs to the belvedere that lets you look down on his creation, you feel a tiny twinge of the sublime – a mini-mingling of terror and awe which, as adults, we normally have only in dreams. When you slide your hand into the velvet gloves of the table game in the work's front room, you experience a frisson of something dark and old, as you do in the cave full of cloth snakes and curry smells. The success of an immersive installation such as this rests on its ability to make you forget the merely real world in which it sits. On this measure, The Edges of the World is a triumph: buses thunder by the Hayward and you simply do not hear them. It is also hugely enjoyable. How often do I get to write those words?

Next Week:

Charles Darwent sees a 20-year perspective of Wolfgang Tillmans' photos at the Serpentine Gallery