The year is 1987 and in a bar in Tuam, County Galway (population 2,997) a raggle-taggle bunch of rock, punk and reggae fans are raising the roof with a raucous mix of pop, country and frantic Irish fiddling.

Fast forward 25 years and The Saw Doctors are one of the most successful Irish bands ever, packing out venues from New York to Sydney.

They’ve played 750 shows in the UK, made almost 100 trips to America, and earlier this year, entertained 50,000 fans at a homecoming show in Galway City – just down the road from the town they still call home.

“It’s unbelievable to think that we’ve already celebrated 25 years together,” says lead guitarist Leo Moran, relaxing at the home in which he grew up and still shares with his father. “I had some vague hope we’d be playing music this long but had no definite ambition. We just wanted to do a couple of gigs, then record a single, then an album and another album...

“It’s been a super way to spend the time though. I’ve enjoyed every minute.”

Over the course of that quarter of a century they have scored 18 top 30 singles in Ireland, including three Number Ones. Their first, I Useta Lover, is the country’s best-selling single ever and occupied the top of the charts for nine weeks. Another, N17, a song about emigration and named after the road which passes through Tuam on its way through the green, rolling fields of Western Ireland, has become the band’s anthem.

Leo, 48, a French and sociology graduate and former teacher, does not fit the lazy stereotype of the happy-go-lucky Irish musician. But then neither does his band. Though their fiddles and big choruses are unmistakably Celtic, the Saw Doctors have never been all that interested in folk.

“We play rock and roll,” says Leo – who started out in a local reggae band. “Our favourite music was always rock, punk and country,” he goes on. “I never really liked traditional music and there wasn’t much of a folk scene in Tuam.”

He admits his efforts in an Irish rock band, which took off after they were spotted and championed by Mike Scott of The Waterboys, have been more successful than his fledgling career as a reggae artist.

“If you stick to your own culture the authenticity carries weight. It has more depth, the emotions are more genuine and it seems to work better.”

So how do the band, who Leo claims emerged from a “repressed, Catholic, conservative, smalltown, agrarian, angst-ridden and showband-infested society,” account for global popularity?

“Our songs are simple and hopefully catchy,” he says. “People can see themselves in the lyrics and make a connection.

“But it’s also down to the fans. They are great. They are so loyal and are a mix of ages and backgrounds.”

The band’s extended 25th anniversary celebrations continue with the release of a ‘best of’ album, 2525.

The record features the band’s best-loved tunes – songs rooted in the peaty soil of their Galway home. They include Tommy K – the true story of local DJ Tommy Kavanagh, forced out of town after defying the bishop’s order and running a disco during Lent; and Howya Julia, which pokes fun at the scandal surrounding a former Bishop of Galway who was forced to resign after news emerged of his affair with an American divorcee with whom he fathered a teenage son.

There is also a 19-date UK tour, which arrives in Oxford on Sunday.

So after all those years trundling around on buses, has the novelty of touring worn off? “The touring is the best part,” he says. “It’s a lovely way to spend time – being on the bus, travelling to places I never thought I’d see and meeting lots of people.

“We’ve been to Australia and all over the States and Scandinavia. And do they still indulge in a little ‘craic’ along the way? “Ah, we have a little refreshment after the shows, as a replacement for sweating,” he says dryly.

“But after we’ve finished a show it can be midnight, and unless you are going to stay up all night you are not going to get up to a lot of damage. Though staying up all night has been known!

“We were younger and more stupid then. We are a bit wiser and more professional now. But not much!

“It can be a bit surreal driving to a gig and leaving straight after, though, so we do make a point of getting out on our days off.

“I am even familiar with Oxford,” he says proudly, though his strongest (or should that be strangest?) memories are of a certain Cowley Road bar.

“We all like the Hi-Lo Jamaican Eating House,” he says. “It’s a great, quirky place. Our first experience was quite interesting, but I think the owner has now got used to us.”

Though, he explains, the band have had to cope with worse than eccentric bar owners.

“Three years ago we were on our way to New York and our bus crashed upstate,” he says relishing a good tale.

“We put all our gear in one pick-up truck and all the people in another and drove to the gig in Manhattan. Unfortunately, though, the one with the gear didn’t arrive. It turned out it was the first day of the hunting season and the driver had gone off with his gun! We were supposed to be playing a show in front of 2,000 people, and had to run around town renting everything.”

Despite his joy of travelling the world, his heart remains in the town he grew up in. “I’m happy in Tuam” he says. “There’s a great sense of community and I’m never bored.

“I live with my dad, who is 93. He used to come on tour with us when he was in his 70s and introduce the band. He was our lucky mascot.

“He even came to Glastonbury with us. It was all quite a surprise for him. The only things he asked when he got there was where he could have a shave and where could he go to Mass!”

And what do the band’s friends in Tuam make of their success? “They take it with a pinch of salt,” he says cheerfully. “There are still a lot of musicians there – though not all are as famous as us.”