A journey into the heart of Shakespeare in the company of director Declan Donnellan and Cheek by Jowl is never less than invigorating. And this new production of the late and complex romance, which arrives at the Barbican after an extensive tour, is full of thought-provoking revelation.

Its greatest gains are in the early scenes where King Leontes becomes convinced that his blameless wife Hermione is having an affair with his best friend Polixenes and unleashes a storm of jealousy that kills his son Mamillius and sees his baby daughter Perdita banished to a far off land.

On Nick Ormerod's spare, effective set, and under Judith Greenwood's queasy lighting which leaves pools of darkness at the edges of the action, Orlando James plays Leontes as a man spoiling for a fight, and never quite sure whether he is pugnacious or playful. His physical restlessness sees him whirring around the stage, boxing with his son (Tom Cawte, excellent) and then actually arranging the bodies of Hermione and Polixenes into the lustful positions of his imagination.

He's like James Cagney in White Heat, psychotic and totally insane. But the production's other blinding insight is that this isn't necessarily a happy family to begin with; Natalie Radmall-Quirke's dignified Hermione may be conciliatory but she is also irritated both by her husband and son; Mamillius throws terrific temper tantrums when he is separated from her.

There's also an utterly magical moment in the trial scene, where she walks over to embrace Leontes and for a fractional second it seems as if tragedy might be averted. Throughout, Jane Gibson's perfectly calibrated choreography emphasises the meaning of each action; here it shifts from absolute stillness to destructive frenzy in the blink of an eye.

The darkness of mood persists in the second half of the play, when the action – after the death of Antigonus, pursued by a slightly disappointing filmic bear – switches to bucolic Bohemia. Here Autolycus (a guitar strumming, audience-baiting Ryan Donaldson) is both genuinely funny but also slightly terrifying as a dead-eyed Jeremy-Kyle-type chat show host, revealing the dysfunction in Perdita's adopted family.

The rain that mars the sheep shearing ceremony, is also in the heart of Edward Sayer's Polixenes, who beats up his own son Florizel when he discovers him literally with his trousers down with Perdita. As the young lovers, Sam Woolf and Eleanor McLoughlin have a lovely freshness, but they are not love's young dream; their lives too feel blighted and uncertain.

These are rich readings. But effective though they are, their cumulative impact is to make the play much less affecting than normal. Without some dignity, Leontes' fall is not a tragedy; without some love, the Old Shepherd's restoration of the daughter who has been lost to her rightful father, loses its magical, healing significance. Peter Moreton is magnificently orotund in the part, but he is required to play against the impulse of the text.

That said, the closing scene, when Hermione's statue comes to life, is sensationally staged. By the light of flickering candles, as the remaining family come together in a painterly tableau of reconciliation, there is a startling, eerie sense that nothing is resolved, a child is still dead, Leontes still unhinged. Like the entire production, it is intelligent and challenging.

The Winter's Tale runs at the Barbican until 22 April. The production will be live streamed here on 19 April.