There are startled looks, anxious screams and by the end of the new, nerve-jangling Doctor Who theatre experience there will doubtless be a few sweating wrecks.

The kids, however, appear to be fine. Exhilarated, smiling and fine.

The theatre company Punchdrunk has opened an event that fits perfectly within the cliched bracket of "highly anticipated" and "hot ticket"; indeed demand for The Crash of the Elysium has been so high extra performances for over-13s have already been scheduled during its run at the Manchester International Festival.

But this is an experience primarily aimed at the Doctor's younger fans. Grown-ups are allowed into this performance only if accompanied by a six to 12-year-old. And thanks to an excitable party from Bridgewater primary in Little Hulton, Salford, the Guardian managed to smuggle itself into one of the previews.

Punchdrunk has already established a reputation for immersive theatre with shows such as The Masque of the Red death and this Doctor Who production, a collaboration with the BBC, continues in a similar vein.

Groups of 25 start their journey in a museum gallery where a kindly, beige-jacketed man called Mr Willard, the sort who always has boiled sweets in his pocket, tells us the history of the Elysium, a ship that sank mysteriously in 1888. Within minutes soldiers storm in. There's a crisis – only we can help.

Everyone is made to run outside as fast as they can, which is the moment you discover just how breathtakingly fast year six children can move.

From there it's a quick change into biohazard suits and full pelt to an exhilarating adventure that sends us back in time to save the Doctor.

As in previous Punchdrunk productions, the attention to detail is impressive. The kids here are really living the experience. They are empowered: solving puzzles, guarding doors and taking decisions. One of the scariest scenes sees us trapped in a darkened corridor as a weeping angel appears to be getting ever closer.

Afterwards 11-year-olds Jack, Naomi and Zoe and Luke, 10, gave their unanimous verdict – they loved it. "It was a little bit scary but cool, a good adventure," said Jack. "I would definitely go back," said Luke. "It was fantastic."

Even teacher Karen Pickard – who alongside a colleague and myself were berated by Captain Solomon and Corporal Albright for not being quick enough – was full of praise for the experience. "They will be talking about it for days," she said with no discernible hint of alarm.

There are undoubtedly scares but they are good scares, followed by something completely different. After a scare there might come the magic and wonder of, for example, a Victorian fairground.

"We have done a lot of work to gauge the right level of scariness," said producer Gabby Vautier.

"One parent rang to say she couldn't get her kids to sleep after they saw it but only in that they couldn't stop talking about it."

The Crash of the Elysium has been scripted by Tom MacRae, a writer so young that "his" Doctor was Sylvester McCoy.

"It is a huge logistical achievement which has meant endless refinements to get it where it is now," he said.

"It is a story for children, it's their story. It's about their experience of Doctor Who and how they would engage with it if they were playing in the playground or in their bedroom with their toys. Except we throw them into something so real and immersive that it's like being in a television show, one you can touch and smell and bang on the walls.

"Any kid who goes will have a day they will never, ever forget," said MacRae. "I wish I was six."

The show is at MediaCityUK in Salford as part of the third biennial Manchester Festival, of which the Guardian is a media partner.

The festival kicked off on Thursday night with the world premiere of Bjork's new show, Biophilia, and will feature Damon Albarn's opera Dr Dee and a new work by Victoria Wood, That Day We Sang.

The Crash of the Elysium will travel to London next year as part of London 2012, the cultural festival celebrating the Olympics.