The Lion in Winter, Theatre Royal, Haymarket

Don't be misled by the mini-history lesson with which Trevor Nunn's belated London stage premiere of The Lion in Winter begins, a sequence of dates, facts and maps that scroll up a decoratively appointed screen and threaten to turn the sumptuous Haymarket Theatre (Nunn's home now across four productions) into an upscale schoolroom.

Set over the Christmas season in 1183, James Goldman's play is deliberately anachronistic, often pretty silly fare in which a rancorous family have a gleeful go at one another, the difference being that this envenomed brood isn't just any Tom, Dick or Harry but, rather, Henry II, Eleanor of Aquitaine and their three variably unhappy and ambitious sons.

Sound like pulpy fun? Goldman's factually sourced "fiction" (his word) is up to a point, especially when Robert Lindsay's Henry is roaring away centre stage amidst the outsized architecture of Stephen Brimson Lewis's sets (pictured below). But after a while it becomes impossible to square this petulant, preening assemblage - Joanna Lumley's Eleanor seems to be preparing for her close-up in some reprise of Nunn's staging of Sunset Boulevard - with the weighty personages of historical lore. Hell, there's more actual gravitas to the TV clan from Lindsay's popular sitcom My Family than is evident from a quintet given over to remarks like, "Hush dear, mother's fighting," that even Patsy Stone might find just a shade too camp.

That's not to say that the material demands undue sobriety but, rather, that its jokiness may come as a considerable surprise to those familiar only with the 1968 film, which won Oscars for Katharine Hepburn and for Goldman himself even though the play's original 1966 Broadway production ran little more than 10 weeks. (Enough, however, to net a Best Actress Tony for its leading lady, the great Rosemary Harris.) Essentially an opportunity for thespian flair and grandstanding that rises or falls on the strength of its leads, The Lion in Winter offers every opportunity for style to eclipse substance. The writing itself is frequently daft: why would a 12th-century monarch cite some bloke called Lear when Shakespeare's play was 422 years away? On the other hand, given that he goes on to reference Medea after the interval, perhaps Henry II made Geoffrey of Monmouth - a roughly contemporaneous source of the Lear tale - his bedtime reading: at last, a king who knows his theatre!

In fact, plenty here suggests that Lindsay might make quite a good Lear, given the growly command with which he sweeps about the stage. Raging at his sons as "three whiskered things" (Lear isn't much kinder to his daughters), Henry tears into the recriminations and resentments in which the play traffics in-between verbal jousts. "You look like Doomsday," he snarls at Eleanor, which may not be a kind thing to say to a self-harming, incarcerated spouse who spends inordinate amounts of time staring into the mirror. The actor's physical looseness, too, rescues the part from the marmoreal aspect that Laurence Fishburne brought to the same role in The Lion in Winter's last Broadway revival, in 1999. There's a discernible spring in Lindsay's step that the play at its most faux-hip - a fleeting homoerotic encounter included - would do well to emulate.

The same doesn't necessarily apply to the rest of the cast, though Tom Bateman (pictured to the right of James Norton and Joseph Drake as his brothers) possesses both the stature and fire for Richard the Lionheart, mum's favourite son. I'm not sure anyone could lend credibility to Goldman's infantilising view of daddy's boy John, himself the subject of a Shakespeare play all his own, and one after a while feels for that fine young actor Joseph Drake having to bounce around the stage as if on an invisible trampoline. (Geoffrey, the third son, barely registers through no fault of James Norton, the actor playing him.) As the French King, Philip, who lures Richard into his bedchamber, Rory Fleck-Byrne has style and dash and is spared the more insipid passages that beset Sonya Cassidy, who plays Princess Alais, Philip's sister and Henry's mistress. Oh, and Richard's would-be wife.

The principal sticking point is Lumley, returning to a ramped-up equivalent of the regal environs that brought her to the West End and Broadway last season in La bête. (In that, she played a 17th-century princess.) Entering the fray like an elaborately garbed Lady Bracknell, she gets the japery of the part perfectly well without ever cracking open the gracious hauteur to get to the hurt underpinning the shoutier passages that make the last half-hour or so of the production such a slog. "We're jungle creatures," Eleanor says, insisting more than once on the barbarism that lies beneath the barbs. But without a leading lady willing to go for the jugular, Goldman's play comes off as a faded jeu d'esprit, less an ageless battle of wills between the sexes than an essay in Plantagenet lite.

• The Lion in Winter at the Theatre Royal, Haymarket, until 28 January, 2012