Narnia – you know the place: lamppost, stone table, forest of snow. CS Lewis' parallel universe exists with such vividness, a whole world of its own, that it's easy to forget what's on this side of the wardrobe. The four Pevensie children – Peter, Lucy, Edmund and Susan – certainly do, staying put for what feels like a lifetime, but so do we, as readers. Narnia lives in our imaginations. It feels all too real.

Sally Cookson's staging, which respects and reinvents the original as did her Jane Eyre, never once lets us lose sight of its context. Rooted in rural England, mid Second World War, Cookson's Narnia becomes an expression of our world, not an unrelated alternative. She casts us all as evacuees, opening with a train journey – suitcase carriages steaming through a countryside of coats – that tears city kids from their parents and deposits them with thick-accented foster families. Her Narnia, like the forest of A Midsummer Night's Dream, is infused with reality. Foster parents double as its ruling forces and its deep freeze, a century old, embodies the chilly, unchanging austerity of a world at war. Our war bleeds into theirs: homes are trashed, civil critters go to ground, woodland spies chatter into tin can phones.

Being both familiar and unfamiliar, it's strange, unsettling and scary, yet wondrous and magical all the same. Cookson and her designer Rae Smith unleash those qualities brilliantly, keying into the story's in-built spiritualism. Lewis intended his Narnia novels as a Christian allegory, but in drawing out its pagan symbolism – natural and seasonal cycles being key – Cookson honours the original and releases something novel and potent.

In a reconfigured, in-the-round West Yorkshire Playhouse, glowing ley lines crisscross over Smith's vast circular stage. They suggest division and danger; cracks in the ice. Carla Mendonça's White Witch, cricking her joints as if cold's crept into her bones, wears a wicker headdress wrapped in spider webs, and Iain Johnstone's alpha Aslan is all Glastonbury spirit: bouffant, beaded and handing out flowers. His free-spirited followers gambol around him, lofting a giant leonine Chinese Dragon high overhead. Even Father Christmas gets in on the act with a semi-shamanistic clog dance as he delivers his gifts.

It all instils a rich theatricality and, with it, real charge. Played as a pageant or ritual, it looks phenomenal, but when characters talk of Narnia's "deep magic," you feel they might summon something for real. For all its open artifice, the room fills up with feeling. Paper lanterns ripple with coloured light overhead, and Benji Bower's supple score, sometimes bursting into rich song, carries the action on a wave of atmosphere: creaking boughs and whistling winds melt into the sunny, sighing folksong. This Narnia is full of noises.

Embracing that theatre lets Cookson mix modes and switch tones. Ira Mandela Siobhan's ferocious Maugrim, all muscle and teeth, body pops like some shapeshifting demon, while the White Witch's minions, led by Amalia Vitale's impish Bog, are a muttering, spluttering comic presence throughout. Dan Canham's choreography can stomp up a storm, before a graceful aerial routine unfurls like the spring. Craig Leo's puppets veer from cute mice to dark, skeletal hordes via a fizzy, delirious, pink Turkish Delight trip as Edmund tucks in.

It allows Cookson and writer Adam Peck to honour the story in full. Rather than refining the plot to suit the stage, they embrace and embody details others might drop – White Stags and Aslan's flight – and the reward is something truly epic. It's unwieldy in places, too vast and amorphous for its own good, and as it unfolds, panto risks creeping in, but at its best, this is brilliant. A Narnia for now.

The Lion, The Witch and The Wardrobe runs at the West Yorkshire Playhouse until 27 January.

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