From Wellington to Gladstone, and Macmillan to Cameron, Eton College has long been a seedbed for British politics and for the diplomatic service. More recently a smattering of television personalities, conductors and Olympic sportsmen have also been able to look back at schooldays spent on the celebrated playing fields. Now though, that famously establishment school near Windsor is increasingly being hailed as a first-rate launch pad for a theatrical career.

Leading Old Etonian actors such as Tom Hiddleston, Harry Lloyd, Eddie Redmayne, Henry Faber and Harry Hadden-Paton are suddenly at the top of the list for casting directors on the most prestigious film and television projects.

This week Hiddleston, star of Steven Spielberg’s War Horse, is in Wales filming Sir Richard Eyre’s Henry IV, along with Faber and Lloyd, the actor last seen in Great Expectations and now appearing in cinemas in The Iron Lady. Meanwhile, Redmayne, of the Golden Globe-nominated film My Week with Marilyn, stars in the BBC adaptation of Sebastian Faulks’s Birdsong, and Haddon-Paton, who appeared in Terence Rattigan’s Flare Path, is shortly to open at the National in She Stoops to Conquer.

So, while the mostly well-connected and wealthy families who send their sons to Eton might hope one day to see them wielding influence in the boardroom, if not in Whitehall, the school’s highly motivated drama department is merrily turning out a growing number of the country’s young stage talent.

For Simon Dormandy, head of theatre at Eton, the success is not simply because there are more roles out there for actors who conform to an “Eton type”. He argues that his stable of stars are just as likely to be playing against the stereotype.

Like fellow Old Etonians Dominic West and Damian Lewis, who made their names with American roles in the television shows The Wire and Band of Brothers, Hiddleston and Redmayne are capable of convincing audiences in roles well beyond their personal experience. As Eton’s head quipped at a school event last year: “When HBO want a gritty, hard-bitten, authentically American character to head up a mini-series they instinctively think: Old Etonian.”

“We really don’t do a line in floppy hair here,” confirms Hailz-Emily Osborne, director of drama at Eton, as she walks down the corridor that links the professionally kitted-out, 400-seat theatre to the more modest studio performance spaces. The walls are lined with production shots from which well-known faces leap out in nascent form.

There is a young Redmayne playing a woman in a sun hat in A Passage to India. An angelic Hiddleston is pictured in a 1998 production of Stoppard’s Arcadia. And Boris Johnson’s younger brother Leo can be seen mugging away.

And there are more bright stars to come, yet to gain wider recognition, says Osborne: Nyasha Hatendi, seen in Garrow’s Law, Sebastian Armesto, Sam Hoare, Julian Ovenden, Will Barrett, and the comedy duo Tom Palmer and Tom Stourton, who recently made the Channel 4 comedy pilot Totally Tom.

This startling line-up of achievement will be celebrated next month by the setting up of Eton’s first drama bursary. “Music has always been part of the curriculum. With drama it is different,” says Dormandy, who learned his trade working with Declan Donnellan at Cheek by Jowl theatre company and who now plans to leave Eton after 15 years to return to “the business” as a director.

Dormandy, known unofficially to the boys as “Dormo”, is pretty clear about what makes drama work so well there. Evidence that other public school actors, such as Old Harrovian Benedict Cumberbatch, are also doing well is beside the point, he claims.

“For me the importance the work has here in the boys’ lives is the reason they do such good work afterwards,” he says. “That importance arises from many things. One is that we don’t do drama just for its educational value. We do a play as a work of art, to be explored at its fullest. Another reason is that there’s an intensity here because the boys are boarding.”

The most able pupils, Dormandy says, are stretched with demanding roles, but all are encouraged to go on to university. “Although with some boys it is clear they would make a mess of university because they are just so desperate to act.”

The school is not trying to produce professional actors, Osborne emphasises, but drama, like everything else at Eton, is taken very seriously. “And if a boy wants to write a play, we take that seriously too,” she says.

The drama department boasts a full-time designer, a carpenter and a manager, as well as a part-time wardrobe mistress. This weekend sees final studio performances of Martin McDonagh’s The Cripple of Inishmaan, before the curtain goes up on Martin Crimp’s Attempts on Her Life. Productions of Ben Hecht’s The Front Page and Alan Bennett’s The History Boys are waiting in the wings for February. The school’s director-in-residence, Rebecca Steel, is also helping to open up the world of movement and dance with productions devised in school.

“They are just boys, I have found, like other young people I have worked with before in Stockton-on-Tees,” says Steel. “But they are all clever and so they are sometimes more analytical in their approach and I need to get them to stop thinking.”

Before Dormandy leaves Eton a new opera is planned, along with a potentially controversial production of sex-themed play Spring Awakening, in collaboration with a girls’ school, and Eton’s biggest Edinburgh festival season yet.

Tellingly, boys do not perform as Etonians up in Scotland. “It would create the wrong expectations,” says Dormandy, who went to Marlborough school. He admits his pupils do have a built-in advantage when it comes to confidence because they know they have already managed to get into a top school. It is a confidence that lends a commanding stage presence. “You can certainly believe it when they play Romans ordering armies about,” laughs Osborne.

“Normally you have to get actors to hold themselves better and be more aware of their posture, but here we sometimes have to persuade them to loosen up a bit,” adds Dormandy.

So who will be the next Hugh Laurie, the Old Etonian currently earning more than anyone else in drama for his turn as an American doctor in House? Informed money appears to be on the young junior boy, or “F Blocker” in Eton terminology, who recently astounded audiences playing Adriana in A Comedy of Errors. The production line continues.

• This article was amended on 13 July 2018 to correct a reference to the name of Boris Johnson’s brother, Leo.