Already armed with the Oscar for starring in Peter Morgan’s “The Queen,” Helen Mirren has said that she thought more than twice about repeating the role. Choosing to do so is the best thing to have happened to Morgan’s play “The Audience.” Transcending mere impersonation, her commanding restraint lends tension to a script that otherwise has little of it. Yet thanks to Stephen Daldry’s immaculately crafted production, a series of smart sketches becomes, if not a play, then a classy night out.

“Every Tuesday,” as the Queen’s Equerry (Geoffrey Beevers) formally intones, “at approximately 6.30 pm, the Queen of the United Kingdom has a private audience with her Prime Minister.” In her 60-years-and-counting reign, she has had weekly conversations with 12 successive government leaders from Winston Churchill to the present incumbent David Cameron.

Not one word of these has ever been documented. So, given that, unlike his “Frost/Nixon,” there are no tapes with which to govern or contradict his invented exchanges, Morgan finds himself with infinite dramatic license. The result is a kind of “Buckingham Palace — Behind Closed Doors” with Morgan choosing to illustrate the Queen’s relationships with just eight of her leaders via dramatizations of some of these weekly meetings.

Beginning unexpectedly in 1995 with floundering Conservative leader John Major (surprisingly emotional Paul Ritter), the play then cuts back to 1952 with the 25-year-old new Queen, in mourning for her father, meeting Churchill (nicely patronizing Edward Fox) for the first time. From there it’s on to 1964 and her first meeting with newly elected Socialist leader Harold Wilson (appealingly contradictory Richard McCabe) and so forth.

Scenes have been chosen less for historical import than for their ability to convey contrasting elements in the Queen’s character. And Morgan’s happy disregard for chronology effectively removes any dutiful sense of historical progress.

Yet the play’s neat structure is also its weakness. Although both Major and Wilson are given extra scenes to show a developing warmth outside of political sparring, everything slides into predictability with characters led on and off for a succession of lightly barbed confrontational one-offs.

To break this up, Morgan resorts to interspersing scenes with a divided self i.e. Young Elizabeth (played, on press night, with eerie assurance by Nell Williams.) She acts as a contrast to, and is interrogated by, Mirren’s older self. But although this adds pathos — the Queen has reigned so long it’s hard to remember she was once a child gradually learning how little freedom she would have — the device is undeniably creaky.

It’s to Daldry and Mirren’s immense credit, therefore, that the evening proves so entertaining.

Rank and privilege are effortlessly apparent as expertly drilled flunkies move furniture, and Mirren’s time-travels are effected by discreet ladies-in-waiting who glide on to change Ivana Primorac’s superb wigs and Bob Crowley’s alternately flattering and ageing costumes. Paradoxically, having the transformations on view adds surprise, with repeated “reveals” as the ladies step away.

Better still, they increase Mirren’s status as someone who has everything done for her. Even without that, against Crowley’s towering, gilded back wall, she effortlessly exudes highest possible status.

From the moment she appears caught in Rick Fisher’s crisp lighting, she conveys a lifetime of keeping her opinions private behind a ruthlessly maintained wall of protocol. Her ramrod-straight back gives her complete authority but she draws audiences in by suggesting an ever-so-faintly wicked degree of asperity simply by tilting her chin a fraction to the right.

Morgan’s script builds an ultimately touching portrait of a woman whose devotion to duty and family — in the widest sense — is absolute. It’s a good deal funnier than expected and Mirren revels in its (somewhat fanciful) Wildean one-liners. But unlike “The Queen,” which played well to both monarchists and republicans, this is a much less balanced love-letter.

It’s certainly being lapped up by U.K. audiences who are delighting in welcoming back not just Mirren but the parade of well-remembered past Prime Ministers. Yet few U.S. audiences will recognize either them or their histories. If this is to have Gotham life, almost every scene will need more than an explanatory tweak or two.

The Audience

Gielgud Theater, London; 984 seats; £59 ($89) top

A Matthew Byam Shaw, Robert Fox and Andy Harries presentation of a play in two acts by Peter Morgan. Directed by Stephen Daldry. Sets and costumes, Bob Crowley; lighting, Rick Fisher; sound, Paul Arditti; music, Paul Englishby; video, Ian William Galloway; production stage manager, Howard Jepson. Opened, reviewed March 5, 2013. Running time: 2 HOURS, 20 MIN.

Queen Elizabeth II — Helen Mirren
Anthony Eden — Michael Elwyn
Margaret Thatcher — Haydn Gwynne
Harold Wilson — Richard McCabe
Gordon Brown — Nathaniel Parker
John Major — Paul Ritter
David Cameron — Rufus Wright
Winston Churchill — Edward Fox
James Callaghan, Private Secretary — David Peart
Young Elizabeth — Nell Williams
Equerry — Geoffrey Beevers
With Jonathan Coote, Harry Feltham, Ian Houghton, Spencer Kitchen, Charlotte Moore, Matt Plumb, Elaine Solomon.