‘Dolphins!” yells Stuart Murdoch, springing across the top deck of the Norwegian Pearl. A pod has been spotted cresting the teal waters of the Mediterranean and the Belle and Sebastian frontman wants to arrange an announcement over the boat’s public address system. But getting involved with the runnings of a 93,000-ton cruise ship as it ploughs towards Sardinia isn’t that straightforward. Murdoch was similarly thwarted last night when he shouted for the ship’s captain from the stage during the band’s first set of the weekend, asking him to sound the horn. Never mind – there will be other chances for everyone to see dolphins. And turtles. And, overhead for a brief moment, flamingos.

After a day at sea on the Boaty Weekender, stuff like this doesn’t seem all that unusual. Since setting sail during Thursday’s late-evening golden hour, a kaleidoscopic cavalcade of surreal loveliness has ensued. As Barcelona disappeared into the haze, the cruise’s Glaswegian hosts played a spine-pricklingly pretty set on the open-air pool deck main stage, beneath cloudless skies in baking heat.

A bill of artists from Belle and Sebastian’s home city and the wider indie scene – Mogwai, Camera Obscura, Teenage Fanclub, Django Django, Yo La Tengo, Alvvays and more – play multiple sets. You can watch some from the hot tub, if that’s your thing. Frances McKee of the Vaselines leads morning yoga sessions. Spanish band Hinds hilariously judge a children’s belly-flop contest. Neither a bar nor a buffet ever seems to be far from hand.

Happy cruisers lap up the atmosphere on the Norwegian Pearl. Photograph: Will Byington

From southern rock sailings to Mexico to EDM excursions to Ibiza and even a short-lived Weezer cruise to the Bahamas, the floating festival is firmly established and increasingly big business. With the Boaty, US promoter Sixthman is investing in its first Mediterranean voyage. Yet Belle and Sebastian claim to have had the music cruise idea as long ago as 1998, just a couple of years after forming.

“The reason we wanted to get on a boat back then was, one, because my dad was a sailor, and, two, because we were having a terrible time with touring,” says Murdoch, reclining on a lounger after all the dolphin excitement. The original notion was to sail from Greenock, near Glasgow, around the British coast. It took 18 months to plan the event and P&O Cruises were attached, but things ran aground.

Almost two decades later Sixthman – which runs the Kiss Kruise – presented Belle and Sebastian with an opportunity at last to launch the indiest cruise that ever sailed, not from the Clyde but on the Med.

“It’s like the geeks won,” Murdoch says with a grin. “The geeks made it to heaven for a long weekend.” It’s also 20 years after the Bowlie Weekender – Belle and Sebastian’s original, land-based festival at Butlin’s in Minehead, which inspired the long-running All Tomorrow’s Parties’ artist-curated events series. It is unclear whether the Boaty will itself become a repeat thing, but nobody is ruling it out. Come to think of it, the Norwegian Pearl feels not unlike a more luxurious Butlin’s in seagoing form. Boatlin’s, if you like.

'We're not big cruise people. I don't even know how to swim'

If you think cocktails and swimwear sound a far cry from Belle and Sebastian’s enigmatic, bookish indie-pop roots, you’re not wrong. Prices starting from around £1,200 per person for the most basic of cabins – inclusive of food but not flights nor alcohol – were prohibitively high for many. But for the 2,000 or so fans from around the world who can afford it, it is a once in a lifetime opportunity to go on holiday with their favourite bands.

I meet Missy Kulik and Raoul de la Cruz from Atlanta, Georgia, at the mandatory lifeboat drill. “We’re not big cruise people,” says Kulik. “I don’t even know how to swim.”

“The last big music excursion we did was Kate Bush in London,” says De La Cruz. “This is our one big trip for a few years.” They give me some handmade pin badges.

Not the Med … Belle and Sebastian in Balmaha, Scotland.

Others have come from Japan, Mexico, South Korea, Scotland, you name it. Tony Wadsworth has even come from New Zealand. “In a few years I won’t remember how much money I spent,” he says, laying back in a hot tub. “I’ll just remember that I was here.”

Shore leave in Sardinia to explore the narrow streets and sandy beaches of Cagliari feels like a bonus. The sun sets over the bay as the return voyage begins. Buzzcocks, led by the indomitable Steve Diggle, thrash out a riotous set featuring a rotating cast of guest singers, in one of their first performances since founder member Pete Shelley died. As the clattering last strains ring out in the fading light, that’s when the flamingos fly over.

Others may have beaten Belle and Sebastian to hosting cruises, but it’s hard to imagine anyone else doing it with so much charm, audacity and sense of happy communality. The fact that a 50th birthday party, several honeymoons and a hen party have been dovetailed with the trip shows how much the band matter in many peoples’ lives. At least two couples are newly engaged before we disembark in Barcelona.

The hosts’ second set of the weekend, this one by moonlight, climaxes rapturously with a 12-year-old kid named Dan from Stoke-on-Trent getting up to slay Queen’s Don’t Stop Me Now at the piano, with Hinds being invited to sing backing vocals on Belle and Sebastian’s The Party Line. There is then a very polite stage invasion. Murdoch again calls for the captain to sound the horn – and this time it loudly blows.

