Back in 1971, at the Citizens Theatre in Glasgow, a budding young assistant stage director by the name of Tim Webb met his wife-to-be Amanda (later to be known as Claire de Loon), who was working as an assistant designer to the great designer and director Philip Prowse.

"We met," Webb remembers, "over a bacon sandwich in the cafe next to the theatre."

Ten years later, along with their friend, composer and musician Max Reinhardt, they established children's theatre company Oily Cart. In the three decades which followed, the company (which is based in south London) has become renowned throughout the UK and internationally for creating a unique brand of startlingly colourful, tactile, musical and interactive theatre for the very young, children and young people with profound and multiple learning disabilities, and kids and young adults with an autistic spectrum disorder. Indeed, the company's work has received such ringing endorsements that Webb was summoned to Buckingham Palace last November to be given an MBE by the Queen.

There is in Oily Cart's work an extraordinary capacity to engage with audiences which many theatre practitioners would consider either hard to reach or difficult to subdue; if you don't have the attention of a roomful of toddlers, the kids' lack of interest becomes quickly and abundantly clear. When it comes to work for pre-school and early years primary school children, the trick, as Oily Cart prove with a skill I have never seen equalled in 17 years as a theatre critic, is to make the children participants in the story.

The company's method – which involves exploration, movement and brain work of various kinds – is familiar to audiences of the MacRobert Arts Centre at Stirling University. Justifiably acclaimed as Scotland's leading arts venue for children and, by Webb, as one of the "premier children's venues in the UK", the MacBob has hosted numerous Oily shows, including Conference Of The Birds (a superb piece for kids with profound and multiple learning disabilities) and How Long Is A Piece Of String (a delightful promenade piece which took young children through a world made of rope and string).

Now Oily Cart are coming to the Stirling centre with their latest work for three-to-six-year-olds. Entitled Ring A Ding Ding, the piece is performed through acting, puppetry and song, and finds Alice in search of her runaway dog. With the assistance of the children in the audience, she travels on land, sea and in the air (even going to the moon) to find the elusive canine. As well as engaging the children in moving physically around the theatre space, the show has, at the centre of the stage, revolving turntables which help to move the action of the story along.

"We wanted to create a piece in which the kids could actually put their fingers on the stage and have their noses in the action," Webb explains. "Every child who wants to can sit right up on the stage and literally touch the puppets and the set – and they do, a lot."

The turntables have been compared to the conveyors which transport food around fashionable sushi restaurants. However, as Webb points out, in Ring A Ding Ding, "there are no motors involved. The turntables are rotated either by the stage managers or members of the cast, but the children are encouraged to join in, so they all push the turntable round. They really like that," he says, with a laugh. "They'd do that all the time if you let them. You have to stop them doing it."

As ever with Oily Cart, however, stopping children from doing something does not involve any form of punitive prohibition. Rather, it simply means giving them something even more interesting to do. And there's plenty to do in helping Alice find the dog.

"The dog keeps turning up on various forms of transport," says Webb. "He turns up on a motorbike. He has to overtake the milkfloat [on which Alice is travelling] on the motorbike; so the kids have to push the outer turntable really fast, and they really like that. Then he's in a motorboat, in which he overtakes [Alice's] paddle steamer. Finally, he turns up in a hot air balloon, in which he travels, followed by Alice, to the moon. Fortunately, we meet the Man in the Moon, who sprinkles moon dust over the children, enabling them to fly to the moon."

This journey entails some crucial interventions by the children, including ringing the alarm bells when the paddle steamer (in which Alice is searching for the dog) gets caught in a whirlpool. The bells alert the mermaid coastguard, who saves the ship, but not without a humorously awkward moment. "The mermaid is really pissed off," Webb explains, "because she's on nights, and they've woken her up."

All of which – interactivity, bold storytelling, wonderful music, imaginative puppets, gorgeously bright costumes and sheer, unadulterated silliness – is quite typical of Oily Cart's remarkable theatre. Here's to another 30 years.

Ring A Ding Ding is at the MacRobert Arts Centre, Stirling University, January 17-21. For further information, and to hear music from the show, visit www.oilycart.org.uk. Sunday Herald theatre critic Mark Brown is editor of the forthcoming book Oily Cart: Impossible Theatre For Young Audiences, which will be published by Trentham Books later this year