Through the smart phone and down the rabbit hole: that's the idea in this ambitious new Lewis Carroll-inspired musical by Blur front-man Damon Albarn, his third project at the MIF, with book and lyrics by Moria Buffini and a production by Rufus Norris, arriving at the National in November, that feels, for the moment, like a glorious work-in-progress.

Although Albarn's beautiful music doesn't sound too much like anything else in musical theatre, there is a piercing lyricism to much of it, some solid rhythmic tropes that coalesce in ensemble images of the real world and the internet of fantasy, where Rosalie Craig's avatar Alice is trapped in a pictorial nightmare of skewed Lewis Carroll figures.

The link here is Anna Francolini's horrid schoolteacher Ms Manxome - aka the Red Queen - who confiscates Aly's (Lois Chimimba) phone and perpetrates a crisis in communication with the internet world. The set-up is very similar to that of Jennifer Haley's The Nether but without the sinister connotations that the internet might be a parallel universe in which it was possible to condone, for instance, child abuse, because it wasn't "really happening."

The idea of the internet as an escape, a safety valve, works differently here because it's created its own victim and is unconditionally shown to be evil and dangerous. Aly as Alice, in fact, has jumped from the frying pan into the fire, a predicament conveyed in Rosalie Craig's pain-tinged vocal lines soaring over the musical numbers.

Aly's real world of tower blocks, grey costumes and mundanity is represented by her cheesy home life. Dad (Paul Hilton) is a gambling addict, Mum (Golda Rosheuvel) is a noisy harridan lumbered with a small cabbage patch baby who pukes voluminously at the slightest provocation.

The lighting and sound of Paule Constable and Paul Arditti create, with the projections, a whirling vortex of coloured vegetation, a sci-fi paradise of exotic colour and magenta-tinged night-time, while choreographer Javier De Frutos makes some telling distinctions between the earth-bound humans and the re-born Lewis Carroll internet zombies.

There's a huge dodo, for instance, peeking out from a towering head with patched on buttons for eyes; a one-dimensional Cheshire Cat whose flat mauve visage is the show's poster image; and Tweedledum and Tweedledee have become a pair of rather nasty pageant queens. One of the best ensemble numbers is a rousing chorus of "Everyone loves Charlie," which gained the instant approval of the clubbers in the first night crowd.

You couldn't imagine a musical more tailored to contemporary consumption than the tragic consequences of trying to recover your smart phone. It's a credit to Norris and co that they make this dilemma so interesting and dramatic, though the overall impression is, at the moment, of something as gorgeously incomplete as Tori Amos's The Light Princess, which was also a much more substantial vehicle for Rosalie Craig at the NT.

But, as with The Light Princess, you sometimes settle for less because of the promise of more. At the moment, the first act is too long and the second, which really starts to cohere into something, too short. But so many good ingredients are in place, not least Tom Deering's musical direction, Katrina Lindsay's amazing costumes and the witty orchestrations of David Shrubsole, showing off Albarn's music in the best possible light with simple plucked guitar lines and some great percussion and brass underpinning.

wonder.land runs at the Palace Theatre Manchester until 12 July and at the Olivier, National Theatre from 27 November. Click here for more information.