The band, who had played a gig at Inverness venue Beyond on Wednesday night, decided to hire a speedboat on Thursday morning and land on the Outer Hebridean island of Taransay, off the coast of Harris, which is featured in the BBC Scotland documentary series.

But the volunteers who agreed to take part in the year-long social experiment declined the offer of a free, impromptu Dodgy gig.

Speaking exclusively to nme.com about the incident, Dodgy drummer Matthew Priest explained: "I had seen the programme on TV and we had been talking about it for the last couple of weeks. When we were touring the Highlands it became more of a reality, just because the public support was there. People were egging us on to do it. They can’t stop you landing on the island, those people are just living there, they don’t own it."

He said they were greeted by one islander and his two daughters when they arrived on-shore and were asked to wait on the beach until the island’s committee met and decided whether to let them play or not. The committee voted 10 to nine against the gig. The band then offered to play a couple of acoustic numbers in the local school building for those that did want to see them, but the locals took exception to a rumour that they were planning to broadcast the gig live on Radio 1 and asked them to leave the island.

Matthew said: "We just said ‘How on earth are we going to do that?’ We had no equipment to do it with!

"They said we were only doing it for the publicity - so what are they doing it for then? A camera crew filmed every single movement on the island, it’s really bizarre, everything is on camera. It’s all for publicity."

"One guy was really nasty, really confrontational. They were saying ‘We’re castaways, we’re not even supposed to see you,’ so we told them to close their eyes. Some people were really upset, they genuinely really wanted to see us. One girl was crying when we left. We really split the camp. We brought strife to 'Castaway'."

The band left the island and arrived back in Stornoway on the Isle of Lewis just after midnight, performing a late-night gig in a local hotel.

A spokesperson for BBC Scotland said: "We can confirm that the band Dodgy visited Taransay yesterday wanting to play a gig for the castaways. After some discussion, the castaways agreed that they had taken part in the project to get away from these sort of things and felt they were simply being exploited by the band’s publicity. They decided by vote that they should not play and the band were asked to leave."

The 35 islanders have been beset by problems since they landed, with the shelters they were building themselves being blown apart by vicious storms, families falling out and some volunteers begging to leave the island.

Dodgy wind up their 25-date tour with shows at Birmingham Flapper And Firkin on Sunday (June 4) and London Dingwalls on Tuesday. Their new single, ‘Feathercuts And Monkey Boots’ is released on Monday.