'The best line I ever wrote," says Billy Roche, "was a 'Yeh'." That line was in Roche's first play, A Handful of Stars. Roche had been writing for seven years, without success. He was in his mid-30s. Before writing, he had been a failed musician.

He had been working on a novel, during which, at one point, the characters found themselves in a snooker hall. That'd make a good place to set a play, thought Roche, who had never written a play, and not seen that many.

The play took shape around the men who spent their days in the snooker hall. The line came when a local policeman named Swan arrived.

"Swan comes in, looks around the snooker hall, which he despises, and says 'Yeh'."

That was all that Swan needed – and Roche needed.

"Ambiguity is everything," says Roche. "Nebulousness; shadowy; 'the suggested' rather than 'the said'… The meaning is there, in the emptiness of things. With that 'Yeh', the actor captured a whole world of meaning."

Roche started out as a singer. In his 20s, he found himself in Reading in the UK, with a wife, Patty, and two young children, trying to catch a break. By day, he "carried the hod on the buildings", by night he played the folk clubs of London, most of which were "a room above a bar with no mic".

"I was gone at seven in the morning, would come home, wash up, and get out to try and make a name for myself. Everything was going into the dream – the jobs meant nothing to me."

The dream? "You kept thinking that 'The Man' was going to arrive with the magic wand."

The Man never arrived. Eventually, Roche gave up on London.

"Patty was just so lonely over there, it was difficult to look at."

Back in Ireland, he kept at the music for a while. It was the late 1970s, and there was a good scene: "There were about 50 bands on the road, passing each other in the night".

He was aged 29 when his band split up. "When you give up, where do you go? There was nothing else."

He started writing. He wrote "on a small manual typewriter, with keys missing: hammering it out".

"About three years in, I woke up one morning, and I was a writer. One dream had replaced another. And I was a young writer, not an old singer."

Roche went at it hard. "Because I was in my 30s, I was learning fast – I'd been around the block." Still, The Man didn't arrive.

He wrote "all day, every day" – for seven years. And then, in the midst of a novel, he found a play.

A Handful of Stars premiered in the tiny Bush Theatre in Shepherd's Bush, London. It wasn't a world away from the folk clubs: a small room above a pub. But it was, and still is, an influential space. And the play was a hit.

This was the dream, finally. "They were delivering the play exactly as I imagined it."

Roche quickly followed the first play with two others for the Bush, all set in his home town, Wexford. In Dublin, Garry Hynes had taken the helm at the Abbey, and contacted Roche to commission him. He walked into the opening night of the third play in his trilogy, Belfry, with his next play already lined up. "It was a beautiful feeling to go in on opening night knowing I had another job."

That play became The Cavalcaders, a piece about a barbershop quartet, with Roche's gorgeous songs in counterpoint to the darkness running through unfulfilled lives.

The earlier plays were revived and staged together as The Wexford Trilogy. "At one stage, I had four plays on on the same day in London."

Those plays are striking portraits of Wexford, steeped in local accents and references, set at a time of claustrophobic conservatism and economic stagnation. They can be played for nostalgia and comedy, but that belies the bitterness in them.

Like Arthur Miller, Roche writes tragedies of small men, of lives blighted by unrealisable dreams and thwarted potential. "These are diamond plays," he says, "hard, rough-hewed."

But he does it with a lighter touch, with an eye for the comic and an ear for a song. "Sometimes, when I drop an audience down so far, my job is to lift you back up."

Roche has started a novel, and is still busy with the legacy of his collection of short stories, Tales from Rainwater Pond, published in 2006. That took him seven years to write. Some of the stories started life as plays, were aborted and found their true form in prose. Now, some of these are finding new life, as scripts.

In September, Roche was in New York, performing an evening of stories from the book, at the 1st Irish Festival. A generous review in the New York Times, and new doors are opening to him there, in a city he has not previously cracked. "I went to New York with two short stories and ended up a playwright," he says.

Another story, Table Manners, was adapted and filmed by Conor McPherson, as The Eclipse; it was recently a hit at the Tribeca Film Festival.

And just premièred in Wexford, before touring to Cork and beyond, is a stage version of the story One Is Not a Number, which takes a tale of mythology and makes it "absolutely particular" to a small corner of Wexford, a nearby pond. Performed by Roche's long-time collaborator, Gary Lydon – who was in that perfect, first cast in the Bush – the story is a blend of subtle social observation and near-burlesque comedy that almost, but not quite, disguises an underlying savagery.

In New York one night during his recent run, Roche noticed a woman in the front row who sat stony-faced throughout. Later, he found himself beside her at the bar. He asked her had she not enjoyed the stories.

"In New York," she said, "we like it right on the nose."

Lyrical, fleeting, enigmatic, Roche's stories don't give it to you on the nose.

"We're in the habit of telling everybody what to think, what to feel," he worries. Instead, these stories celebrate "that Chekhovian thing – a look, a moment". Or, as he learned many years ago, simply a "Yeh".

'One Is Not a Number' concludes its run at the Wexford Arts Centre tonight before beginning the first leg of a national tour at the Granary Theatre, Cork from Wednesday