Lessons in love: David Eldridge is back with a play about the tangled sex lives of teachers

The history of stage drama is littered with embarrassing stories of theatres that failed to spot the winners they were offered. The Royal Court rejected Angels in America, the greatest play of the late 20th century. Hampstead Theatre declined My Night With Reg, the key tragicomedy of the Aids era. And the Bush commissioned and then turned down David Eldridge's Under the Blue Sky, one of the best and most beautifully constructed plays to have emerged since the millennium.

Eldridge had the last laugh, however. When it was presented at the Theatre Upstairs in 2000, the piece rightly garnered gongs and glowing reviews. And though we live in what he describes as "the culture of virginity" – where new plays rarely get a second staging – Under the Blue Sky looks set to establish itself as a staple of repertory. There have been several revivals and next week sees its West End premiere in a production with a Rolls-Royce cast, including Francesca Annis, Catherine Tate and Chris O'Dowd.

By turns incisive, uproarious and deeply moving, the play is like a cross between a dramatic triptych and a subtler version of Schnitzler's sexual daisy chain, La Ronde. The twist is that all three couples are schoolteachers. In the first scene, Nick (O'Dowd), a shifty, on-the-make English teacher, tells his colleague Helen that he is opting out of state education. She realises with bleak fury that this career move is also his way of bailing out of their relationship. In the blackly riotous middle episode, we encounter Michelle (Tate), who's been Nick's lover at his next school. Now dumped and drunk, she's resolved to get even via a sex-romp with Graham Ibbotson, the "Little Hitler" of the CCF, a virginal bore and staff-room laughing stock. And in the touching final scene, the friendship between two senior teachers, Anne (Annis) and Robert, flowers into full love despite the 16-year age gap. During their discussion, we discover the ultimately tragic fate of the exploited, clinging Helen.

Eldridge went on to compose such diverse and first-rate theatrical fare as the hugely successful stage version of the Dogme film, Festen; Market Boy, which was the first play by a writer of his generation to storm the Olivier; and two eloquent Ibsen adaptations (The Wild Duck and John Gabriel Borkman) for Michael Grandage at the Donmar. But when he submitted Under the Blue Sky to the Bush, he thinks they were taken aback. He'd shot to recognition there at the age of 22 with Serving It Up, a grittily funny drama about young, disaffected no-hopers in Hackney. "The new play wasn't what they were expecting. It was the first time I'd experimented with form or described a different class. So it was a double whammy of surprise for them."

He reveals that his original plan for Under the Blue Sky involved only one teaching couple. "It was going to have a similar structure – first drink, drunkenness and then the hangover the morning after. I remember not being very satisfied with it. I was literally on the top of a bus when it struck me that I could keep this form but have a different couple at each stage. I'm a big admirer of Wallace Shawn's A Thought in Three Parts and I really like the way that title describes a possible shape for a play".

The piece was motivated, to some extent, by Eldridge's dissatisfaction at the way teachers had been depicted in drama. "They seemed to be portrayed as either faux-idealistic types, like Kyra in [David Hare's] Skylight or as reactionary ogres such as Mr Bronson on Grange Hill." He'd always loved listening to his teacher friends gossip about their colleagues over a bottle of wine, but he'd never seen their sort in a play.

The private lives of the profession have since been tackled in TV series such as Teachers and Waterloo Road. But Under the Blue Sky is exceptionally acute about the subject. Eldridge perceives teaching "as a metaphor for unrequited love", an experience that recurs throughout the play. "You can be in proximity to youth as a teacher but you can't reclaim your own. It can feel like standing on the sidelines watching this constant turnover of young potential." The situation is complicated by the contradictory demands on teachers. It's supposed to be the noblest of callings, yet the job can turn into underpaid, dangerous social work. Under the Blue Sky shows how these factors affect the love lives of the practitioners.

A working-class Essex lad, Eldridge divided his time as a teenager between his posh, independent school (to which he'd won a place by exam) and a job flogging shoes on Romford market, a location which became a microcosm of the boom-and-bust Thatcherite Eighties in his play Market Boy. Until he reached the sixth form, he felt out of place at Brentwood School. "I'm not hamming this up but my dad used to earn so little as a shoemaker that there were times when money would even be scarce for train fares and it felt like there was this mad disparity between my education and my home life."

But it was thanks to the school's theatre club that, at the age of 17, he got to see his first play. It was Nicholas Hytner's RSC production of King Lear at the Barbican and it changed his life. So, when I ask if he'd accept an invitation to be guest speaker at prize day, he says yes, because he'd like to talk about that mixed experience – unhappy for much of the time and yet transformed positively through being given contact with great art. Eldridge remains refreshingly open and unspoiled by success. Uncommon ability with the common touch: it's a captivating combination. He's not the type who'd allow caution about his career to deter him from speaking his mind – which he often does as a member of the Monsterists. This is a group of young-ish playwrights who campaign to see new work liberated from the restrictions of the black box studio. "It makes me cross," he declares, "that there's been the preconceived notion that what belongs on the big stages is the kind of bang-on-the-nose, state-of-the-nation play that confirms Guardian readers in their prejudice."

But the culture is, Eldridge suggests, "discreetly changing". There have been part-devised pieces, such as War Horse and Market Boy, mounted in the Olivier, where Rebecca Lenkiewicz's new play, Her Naked Skin, is about to open. And the flagship companies are realising that it's in their interest to foster the aspiration to write for large spaces that has been crushed in the young by the years of confinement. He applauds the RSC where, under Michael Boyd, the dramatists on attachment have their imaginations fired through involvement with the classic main stage productions.

Eldridge has just finished a new play on a political theme. Under the Blue Sky registers how public events – an IRA bomb in Docklands, a love story from the Great War – impinge on private lives. But as the playwright acknowledges, it was written during a period of relative security. He's fascinated by how, viewed from a post-September 11 perspective, the piece comes alive differently. Beginning with the bang of a terrorist explosion, the triptych ends with the sounding of the last post. "When Under the Blue Sky was first produced eight years ago, boys in Union Jack-draped coffins weren't being unloaded at Brize Norton," he notes ruefully. "What sounded like a nostalgic memorial then, now sounds as much like a memento mori."

'Under the Blue Sky', Duke of York's Theatre, London WC2 (0870 040 0046), to 20 September