There’s an inherent weirdness to the relationship between a Prime Minister and the Queen – especially in the case of Margaret Thatcher. Here were two women, born just six months apart, whose surface similarities ended there. One was defined by birth; the other could never have been defined by birth. One was an agent of stability; the other could barely see an apple cart without tipping it over. And so on. Yet still they had to meet on a more or less weekly basis, over tea in Buckingham Palace, to talk through the business of state.

Moira Buffini’s play Handbagged, which has just transferred from the Tricycle Theatre in Kilburn to the West End’s Vaudeville Theatre, glorifies in this weirdness. In fact, it intensifies this weirdness. We don’t just have the Queen and Thatcher on this sparse stage; we have two Queens and two Thatchers. One of the pairs is younger, acting out the conversations that might have happened, all things considered, during Thatcher’s three-term premiership. The other is older, plucked from some time in the nineteen-nineties. There are no barriers of time or space. They talk among themselves. They talk to us, the audience. Other actors come on and talk about their roles as roles. Like I say – weird.

It’s also extremely funny. The tone is established right from the off, with Thatcher (the elder, I think) explaining why she would prefer not to sit down: “I would be proud if this word defined me: NO!” When the Queen enters to offer a chair, she repeats: NO! From there, we have both Thatchers swooning at a Stetson-ed Ronald Reagan (“Ron!”); a mischievous Queen on the hunt for political gossip; and two male actors, Jeff Rawle and Neet Mohan, playing everyone from Arthur Scargill to a shoulder-padded First Lady, as well as being the fourth-wall-demolitionists-in-chief.

There is seriousness underneath the comedy, however. Buffini strives to show us what the relationship between Thatcher and the Queen might really have been like – a task that involves a good deal of supposition, but supposition that, as Vernon Bogdanor writes in the programme notes, is “not entirely fanciful”. In particular, it ably highlights the Prime Minister’s nervousness not just at meeting the Monarch, but also about doing things properly. At the end of their first conversation together, she alights on the subject of clothing, and how to avoid wearing outfits that either clash or are too similar. A trifle, perhaps, but one that’s in keeping with the Thatcher described in Charles Moore’s book:

“Mrs Thatcher was ‘nervous about how to comport herself with the Queen’ and worried by a series of occasions in which she would either upstage the Queen by mistake or be overshadowed by her. There was a problem, though Mrs Thatcher would never have put it like this, of ‘Who’s the star?’”

When it comes to Handbagged, there’s also a problem of “Who’s the star?” – although in the best possible sense. There are six actors in the play and all are, at the very least, very good. I’d say Rawle, who is mostly Denis Thatcher alongside other characters, raises the stakes to excellent. But it is Fenella Woolgar who, as “Mags,” the younger Thatcher, really stands out. The voice, the graceful-yet-strained mannerisms, they’re all there. But this is no mere pastiche: Woolgar performs the role with enough smiling knowingness to make it something else.

But what about the politics? It’s a question that’s unavoidable with a play such as this. And the answer is clearly somewhere to the left of Thatcher. The Queen is too often, and too conveniently, portrayed as a conscience to her Prime Minister’s constancy. Whilst the Prime Minister, with her recourse to quoting Hayek, is an easier source of laughs. But if you cannot get along with that, then good luck getting along with Britain: on the whole, we rib our politicians and esteem our Royal Family. Besides, Handbagged’s ribbing of Thatcher is clearly mixed with respect. The Brighton bombing and her resignation are treated with particular sympathy.

A year on from the Lady’s death, perhaps some would prefer a more straightforwardly reverential production. But Handbagged is a fine tribute, in its way. Two historic figures, four actresses, four bouffant hairstyles. It will be some time before another Prime Minister gets the same treatment.

> Handbagged is at the Vaudeville Theatre until 2nd August.