It’s day five of rehearsals for Daisy Pulls It Off. In slink the Upper 4th Form of Grangewood School for Young Ladies, clutching coffees or their heads, comically contrite after one too many lashings of pop on a class outing the previous night.

The outing was to David Mamet’s Glengarry Glen Ross in London’s West End. “It was very male. There was a lot of this …” declares head girl, AKA director Paulette Randall, slouching back into a dramatic manspread. “Ah but it was lovely, lovely …” chorus the girls, pulling themselves up a little tighter in their chairs.

The “girls” in this production of Denise Deegan’s award-winning boarding school comedy span three decades in age and include one boy, as well as a small furry fox, called in to ventriloquise a pupil named Dora. It’s the sort of ingenuity that’s required to mount an intimate fringe revival of a show that originally ran for three years in the West End with a cast of 17.

A parody of Angela Brazil’s boarding-school novels of the 1920s, Daisy was a surprise hit, which began life at Southampton’s Nuffield theatre in 1983 and went on to make the names of a glittering roll call of promising unknowns including Samantha Bond, Lia Williams and Gabrielle Glaister.

“When I got the script, I said ‘Why have they sent this to me?’” says Randall, who deputised for Danny Boyle on the London Olympics opening ceremony. “My kneejerk reaction was that I wouldn’t want to go and see a bunch of girls being all jolly hockey-sticks. And then I thought they wouldn’t expect me to do it as it was written.” She quickly realised that the pocket-handkerchief size of the stage offered a chance to reinvent the play. “It’s not in a proscenium arch and there’s no revolve, so we’re doing it as a bunch of girls putting on a show in a school assembly.”

The clincher, she says, was “being with a bunch of women having a laugh. That’s how I started out really – doing sketches and getting my friends to perform them.” It all began to go wrong when, in 1982 at the age of 21, she had a play, Fishing, staged at the Royal Court. “I started taking myself a bit too seriously – saying ‘I am a Theatrician’…”

Randall went on to become one of the UK’s leading female directors, heading the black theatre company Talawa, chairing the board of the female prisoners’ ensemble Clean Break and becoming the first black woman to direct a play in the West End, August Wilson’s Fences, in 2013.

Though comedy has always played an important role in her life – her TV credits include the sitcom Desmonds and the sketch show The Real McCoy – she was into her 50s before she discovered the broader pleasures of pantomime, through two well-received rock’n’roll pantos at the Stafford Gatehouse theatre. “I thought, this isn’t what I do – I do drama and comedy. But I found I loved it.”

Daisy’s a bit of a nod to panto, pipes up actor Clare Perkins (EastEnders, Family Affairs), who has turned up in squashy hat, shades and breeches like a hungover Jack in search of a beanstalk. “It has the two ugly sisters and the beautiful and good heroine.”

“It’s a licence to ‘do the acting – let’s just pretend to be someone tonight’,” quips Pauline McLynn (Mrs Doyle from Father Ted). “Paulette is always saying ‘more’: the word you never hear,” riffs Perkins. “It’s very, very exciting that … ‘Just. Do. More,’” adds Shobna Gulati (Anita in Victoria Wood’s Dinnerladies).

Part of the reason for this licence to overact is that the classroom scenes require a lot of “back acting”, as the pupils are facing away from the audience and towards the fearsome Miss Granville. “Make it bigger … even bigger,” commands Randall, as they squirm, snigger and jostle for attention, uniting in a communal shoulder-sneer at Daisy’s breathless recitation of a naval ode.

“Mind you,” cautions the director, “By the time an audience sees it the ‘more’ might have been taken out” – as indeed might Dora’s fox persona. The point is to distribute Dora’s lines among the cast.

They all agree that the extravagant retro spiffiness of Daisy chimes with a society that has staked its future on a return to a mythical innocence. In Randall’s words: “All those Brexiteers saying we want to go back to the time before, when most of them wouldn’t have experienced it anyway – it’s all from books.”

Though the comedy is broad, it’s not devoid of social conscience – indeed the plot revolves around it: new arrival Daisy is a scholarship girl, and as one appalled “dormi-mate” remarks, “Scholarship girls – they’re poor. Perhaps not intellectually, but definitely morally.” .

“It’s not Chekhov, so let’s not pretend it is,” says Randall. “But I’m a black working-class woman from south London and incredibly proud of it, so it’s important to me that there is a sense of social justice in there – that just because you’ve got a posh accent doesn’t mean you have a great brain.”

Mention of posh accents gets the “girls” going again, reminiscing about their own schooldays and their memories of being 14. Gulati, whose family emigrated from the Punjab to Lancashire, has fond memories of devouring boarding-school stories beneath the blankets for their sense of camaraderie and for adventures that didn’t happen at her Oldham grammar school.

Her nostalgia for “that stage between girlhood and adulthood with no exams when I was completely, stupidly naive, but happily so” provokes a snort of laughter from Perkins, for whom being 14 on a Peckham housing estate in the 1970s was all “2 Tone and Rock Against Racism and running around with raging hormones thinking I just wanted to leave home – and then I got pregnant at 16 and did leave home.”

Twenty-five-year-old north Londoner Anna Shaffer, who came to fame as the besotted Romilda Vane in the Harry Potter films, wasn’t even born when the play premiered. Her Daisy is a picture of innocence, but Shaffer disconcertingly throws in: “It’s the age when you discover you can lie, because you’re growing up and you’re a bit more of a manipulator than you were.”

“Yes, well,” sniffs Sligo-born, convent-educated McLynn with mock disdain, “some of us take it to the Nth degree and lie for a living. That’s acting.”

The great set piece of the play is a hockey match, which particularly pleases Gulati, who boasts of acquiring “two fat knees” from the sport and having once been the proud possessor of a hockey stick with her surname stamped on it. “It was made by a Gulati in India.”

This revelation prompts a lively debate as to who invented the game, only resolved when someone has the brainwave of consulting Google. “OK, so Canada actually invented hockey,” concedes Gulati, who has put up a spirited case for India. “We’re just incredibly good at it.”

As the wisecracks fly around the rehearsal room, it becomes increasingly hard to work out who is in character as whom, given that most of the cast play at least two people. “We’ve got a licence to play every stereotype in the book,” says Gulati, happily. “They’re not stereotypes, they’re archetypes,” Randall fires back. “I might argue with that,” replies Gulati, “because we’re children playing what they imagine children to be like, so we can be stereotypes and archetypes.”

Even at 10am, with a hangover, it’s all very silly and very good fun. “A lot of the time we’re not proud of being silly,” says Randall. “But we should celebrate the fact that we can make each other laugh – it’s such a beautiful, healing thing.”

• Daisy Pulls It Off is at the Park theatre, London, from 5 December to 13 January. Box office: 020-7870 6876.