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The Lion, the Witch and the Wardrobe, Kensington Gardens, London; Ragtime, Regent's Park Open Air Theatre, London; Atigone, NT Olivier, London

Two book adaptations join the season's outdoor productions, while a Greek tragedy exiles Antigone to Sixties corporate America

Now here's a pearl of wisdom. "Don't go trying the same route twice," the Professor advises in The Lion, the Witch and the Wardrobe, the CS Lewis children's classic adapted and staged by Rupert Goold. The kindly prof (Brian Protheroe) is suggesting how his wartime wards – Lucy and her evacuee siblings (four youthful-looking actors) – might find their way back to the magical kingdom of Narnia. On another level, he's talking about how to remain imaginative.

Yet Lucy doesn't agree. Glimpsed in a coda, as if cueing an instant sequel, we see her step once more into the dark oak wardrobe that rises out of the spectacular spinning stage in Kensington Gardens' big top. Winning formulas invite repetition. Lewis himself – a Christian and a fan of Greek and Nordic legends – recycled elements from folk myths and redemption sagas.

Even so, Goold's production will look derivative to anyone who has seen other recent family hits. The puppetry blatantly cribs from War Horse, and other ingredients are traceable to The Lion King, The Lord of the Rings and The Snowman. Has Goold been juggling too many projects? Threesixty Theatre doesn't seem to be getting his best here, with surround-projections that are merely distracting and actors' miked voices disconnected from their bodies.

Things improve, however. Adam Cork's musical numbers grow less cheesy, more operatic. Some of Tom Scutt's designs are winningly inspired by tribal costumes and masks, and Aslan is eerily magnificent, like a risen corpse with bare rib bones, grey bark for flesh and a mane of autumnal oak leaves. In all, though, short of miraculous.

Meanwhile, in Regent's Park, Timothy Sheader imposes a bold directorial conceit on Ragtime, the musical adapted by Terrence McNally from E L Doctorow's novel about racial injustice in early 20th-century America. Open Air Theatre's stage is a grim mound of rubble, with allusions to 9/11 and a charred billboard poster reading "Dare to Dream".

In a mix of 21st-century and period costume, Sheader's actors play out this sociopolitical epic which interweaves the lives of a well-off Wasp couple with those of African-American and East European immigrants. The latter start out with high hopes for a multicultural future, only to run into shocking xenophobia and exploitation by fat cats. The wronged ragtime pianist, Coalhouse (Rolan Bell), then joins a terrorist cell, with rucksacks of explosives.

The director flags up ongoing reverberations, although some of his parallels are questionable. The scorched "Dare to Dream" billboard isn't sardonic, by the way, for the chorus ultimately aspire to a peaceful utopia. The problem is that the songs, scored by Stephen Flaherty, are mostly bland anthems. And only Claudia Kariuki is unforgettably poignant as Sarah, Coalhouse's sweetheart, singing a lullaby like a sighing ghost.

In Sophocles' retribution tragedy Antigone – staged by fast-rising director Polly Findlay – Oedipus's orphaned daughter is the enraged freedom fighter, breaking laws imposed by her ruling uncle, Creon, which she considers inhumane. He has forbidden any burial rites for her brother Polynices, a military enemy.

This modern-dress production starts with a tableau. Christopher Eccleston's Creon and his staff sit crammed round a screen, bringing to mind that photograph of President Obama, Hillary Clinton and others viewing the raid on Osama bin Laden's compound. Oddly, though, the furnishings in their glass-walled offices evoke 1960s America.

Either way, the setting doesn't fit with Don Taylor's otherwise fine translation when it alludes to stonings and Antigone's being buried alive for her transgressions. Creon's Thebes is closer, surely, to a Taliban regime.

Jodie Whittaker's Antigone is fierily rebellious, though her grieving needs more intensity, and Eccleston is oddly underpowered as a stiff-backed bureaucrat, albeit with one hair-raisingly violent outburst. Yet the direction is elsewhere impressive, Findlay choreographing fluid scene changes on the Olivier's huge revolve.

'The Lion, the Witch and the Wardrobe' (0844 871 7693), to 9 Sep; 'Ragtime' (020-7494 3665), to 8 Sep; 'Antigone' (020-7452 3000), to 21 Jul

Critic's Choice

At Bath's Ustinov Studio (to 9 Jun), In the Next Room (aka The Vibrator Play) is an ultimately poignant though humorous portrait of a 19th-century doctor treating female hysteria but neglecting his wife. At London's Royal Court (to 9 Jun), Victoria Hamilton is superb in Love, Love, Love, Mike Bartlett's portrait of Sixties hipsters turning into selfish, well-off retirees.