It's sometimes hard not to be cynical about J. K. Rowling's success: the seven novels that sold over 450 million copies; the Hollywood franchise that launched the careers of film stars, the theme park, the HP shops, the merchandise. These days it's not just the T-shirt you buy after you've "done that". It's easy to imagine that every decision relating to the Potter world-dominating brand is a commercial one. But that's not true. In fact, Rowling is in danger of giving globalisation a good name.

Here, the decisions made by the author and her co-writers Jack Thorne and John Tiffany, who also directs, place art above spectacle. Which is not to say that there are not spectacular moments - the fight scenes feature jets of fire that streak across the stage like dragon's breath. When the plot demands travel to a different dimension, the physical world and everything in it wobbles like jelly - an extraordinary effect that will make you dizzy.

As for that cloak-swishing moment, it occurs on platform nine and three-quarters at King's Cross station. Children are about to board the Hogwart Express and, in one blink and a choreographed twirl, their clothes transform from multicoloured teen civvies to the black-caped school uniforms of the school of wizardry. It prompts the first of many gasps from the audience.

But what keeps this five-hour, two-part play moving as fast as a runaway Hogwarts Express is the new story, about which it is impossible to say much without spoiling it. Harry, Ron and Hermione are now grown-ups. Harry is head of Magical Law Enforcement, a role he finds easier than being father to his 14-year-old son, Albus.

Growing up is the theme. How does a child emerge from the shadow of his or her parent - especially when the parent is the famous Harry Potter? Scorpius, the son of Harry's former childhood enemy Draco Malfoy, is equally saddled with a father's reputation. The writing is staggeringly efficient at establishing all these narrative threads.

But the triumph is that Tiffany's production is pure theatre. In that sense, this the future of spectacular storytelling. The effects are special but at no time are they allowed to dominate. It would have been so easy to have given this show the blockbuster shock-and-awe treatment. But the creators deliver something altogether more nuanced, tender and moving. For instance, the floundering relationship of two schoolchildren is portrayed with a ballet of moving school staircases on which the students ascend and descend without ever quite encountering each other.

As the adult Harry, Jamie Parker transmits the burden of being the world's most famous potent wizard. A terrific Noma Dumezweni as Hermione provides a pleasingly short-tempered intellect to the proceedings, while Sam Clemmett as Harry's son Albus is brimful of adolescent surliness.

But the star is Anthony Boyle's Scorpius, a boy whose heart is hemmed in by his father's austere brand of love, but who nevertheless deals with growing pains of youth with as much wit as he does wizardry. If Rowling were looking to hand on Harry's wand to a new adventurer, here he is. Though how you do that while keeping the commercially crucial name of Harry Potter is a question well beyond the knowledge of most Muggles.