@ Kings Theatre, Edinburgh, until Sat 7 Nov 2015

Despite its cringeworthy title this is an effervescent and thought-provoking show ostensibly about the fraught relationship between the present Queen and Prime Minister (1979-90) Margaret Thatcher. But what might have been a knockabout farce is richer fare by far.

There are two queens and two prime ministers – the trim, brown-haired Elizabeth of 1979 (Emma Handy) welcoming the strident new PM (Sanchia McCormack) and then the older matronly Queen (Susie Blake) and a more regal, elder-stateswoman Maggie (Kate Fahy). Each comments on the others’ memories which are severely hamstrung by revisionism. Fahy gets Mrs T down to a, well, T with her strangulated diction. The lady says of her flapping male ministers, ‘I could pin them, wriggling, with my gaze.’ The four main roles are supplemented with two others – Richard Teverson and Asif Khan playing everything from palace footmen to Ronald (and Nancy) Reagan. Khan is especially effective as the audience’s conscience.

The later Thatcher, famously clad by Aquascutum, took on a magisterial hauteur that made Queen Elizabeth seem positively dowdy and down-to-earth. ‘Power is an intoxicant. You mustn’t imbibe too much,’ remarks the Queen. The consensus – flamed by the newspapers, especially the pro-republican Murdoch press – depicted Elizabeth and her first minister in constant clashes. Maggie was the smart parvenu grammar school girl who was a scientist and a barrister and Lilibet the one who “never went to school.” The Queen was said to have been flummoxed by Thatcher’s lecturing and lack of any sense of humour.

The Tricycle Theatre’s Handbagged requires a lot of careful listening and director Indhu Rubasingham keeps the wordy text taut and alive. The dramatically monochrome set (by Richard Kent) is six parts Union Jack to two parts spider’s web. Throughout, the public perceptions of the two women are laid bare. What Thatcher thought and did are well known thanks to volumes of political biography. The playwright Moira Buffini has to guess about the inner workings of the Queen (much of the text is lifted from contemporaneous speeches and broadcasts).

But the story is told with great relish and no viciousness; that’s not to say that the sideswiping one-liners don’t come thick and fast. Says the Queen of Attila the Hen: ‘for a Methodist she is remarkably un-Christian.’ There’s astute political comment too – from the bombing of Libya to the dangers of an unregulated press.

As a romp through recent history Handbagged probably won’t change minds. There is a supreme irony about the Queen talking about the importance of an equal society when she is one of the richest women in the world. Our current era of austerity and oligarchs with a government of heartless Old Etonians can easily be traced back to Thatcher’s socially divisive policies. And sadly that’s no laughing matter.