The Audience (Apollo Theatre)

Two years after Helen Mirren opened as the Queen in Peter Morgan's cunning play about the informal weekly meeting between the monarch and her prime minister – she's currently reprising the role on Broadway – Kristin Scott Thomas succeeds on the throne with her own special brand of twinkling irony and glacial dignity.

It strikes me that both actresses present a portrait of the Queen that is both more calculating and more intimidating than the real woman. And Scott Thomas, considerably younger than Mirren, has a more playful and frostier edge about her. Whereas Mirren visibly warmed towards both John Major and Harold Wilson, Scott Thomas patronises the first and amuses herself with the second, as though he were one of her corgis.

Those dogs still bound across the stage in the mist-laden Balmoral scene in a flash of corgi orgy; Stephen Daldry's smart production and Bob Crowley's ingenious setting of the receding perspectives in Buckingham Palace are still in good order, and the costume and wig changes remain a technical wonder.

But I don't think the interruptions of chronology are so well marked by Scott Thomas, whose performance is more fluent and less poignant throughout. The scenes with her younger self – played by Marnie Brighton (one of three young Elizabeths) are less resonant and ghostly.

David Peart, who played poor old Jim Callaghan first time round, has joined the royal household as the equerry and Callaghan has been subsumed, as in life, by New Labour: a smugly gawping Tony Blair (Mark Dexter) now prefigures David Robb's anguished Anthony Eden's defence of the Suez adventure with similar excuses about the Iraq invasion, and the show has a great new laugh as a result.

Dexter then doubles his Blair with an astonishingly accurate lookalike David Cameron, a smoothly fidgeting operator who has perfected a superior line in deference but doesn't know when to stop rabbiting on about Greece and the financial crisis; HMQ is seriously slumped on her gilt-edged chair by then.

No chance of 40 winks with Mrs Thatcher around, and Sylvestra Le Touzel storms on in a Heseltine hairstyle like Nicola Sturgeon in a force ten gale, seething over a supposed leak from the palace. Scott Thomas turns this onslaught around almost masochistically to her own advantage and an implication of racist remarks on South Africa ("That was Denis," snaps Thatcher).

Nicholas Woodeson is a chaotic but likeable bumbler of a Harold Wilson – twin comic of Mark Hadfield's Wilson in Made in Dagenham – David Calder is a magnificent and kindly old Churchill and Gordon Kennedy a looming and untidy, physically awkward Gordon Brown. From the minute we meet Michael Gould's John Major, bleating on about his childhood with that cheap haircut and those mimsy gestures you do think – well, she could write a book about this shower. Or at least appear in a play with them.

The Audience is booking at the Apollo Theatre until 25 July 2015