Willie Nelson is just one of the artists rushing to cancel gigs at SeaWorld after seeing Blackfish, the documentary about killer whales who have attacked their trainers.

Heart are an unlikely bunch of revolutionaries. But the American soft rockers' decision to cancel a concert at SeaWorld in Florida may mark a turning point in the relationship between humans and one of the most magnificent mammals of the ocean. The band this week joined Willie Nelson and Barenaked Ladies in cancelling shows at the Orlando theme park because they had watched Blackfish, a film about Tilikum, a five-tonne male orca that has been involved in the deaths of three people. This modest yet riveting documentary has made ever-bigger ripples across the pond since its premiere at Sundance earlier this year, with an audience of 20 million recently watching it on CNN. It is now on the Oscar longlist.

Tilikum's plight – enduring violence from other captive whales and forced to entertain crowds in return for fish ever since he was captured in the wild in 1983 – is vividly depicted by former trainers. The film's conclusion is inescapable: we have no business keeping such large, intelligent mammals in such crippling confinement. We too might get a little psychotic, it suggests, if we were imprisoned in a bath for 30 years.

Blackfish, a Native American term for the orca or killer whale (actually a member of the dolphin family), began with an innocuous premise: Gabriela Cowperthwaite, the director, wanted to examine how people relate to large predators. As Cowperthwaite, who lives in California, stresses, she is not an animal rights activist and did not intend to make a controversial film. "I couldn't have been more naive about the situation in SeaWorld," she says. She regularly took her twin boys there as a treat. "I'd see hundreds of children smiling and think, 'How can something that makes people so happy be such a bad thing?' All of us are complicit, starting with myself."

SeaWorld is the slickest of what Cowperthwaite now views as aquatic circuses. The company owns 12 US theme parks and its shtick – orcas leaping to lights and music alongside their trainers – may make many adults cringe, particularly in Britain, where there are no dolphins in captivity. But in the US, more than 11 million people visit a SeaWorld each year.

When Cowperthwaite read news stories about the death of Dawn Brancheau, an experienced trainer killed while performing with Tilikum in 2010, she was stunned by a barely reported fact: Tilikum had been involved in two earlier deaths. "This story was hiding in plain sight. Once you learn the truth, it becomes your mission to tell it. The facts are so indisputable. This is an industry that has operated untouched for 40 years and it governs itself. There's no true oversight of places like SeaWorld."

Blackfish has belatedly provided a window into the aquarium. The story of Tilikum's life – and Brancheau's death – begins with traumatic footage of orcas being captured in the wild to establish parks such as SeaWorld Orlando, founded in 1965. Although wild capture was outlawed in the US in 1972, orcas continued to be seized in foreign waters: Tilikum was caught, aged two, off Iceland in 1983. His early life was spent in a cramped Canadian park. When part-time trainer Keltie Byrne slipped into the pool containing Tilikum and two female orcas in 1991, she was killed. The park was closed and "Tilly" was snapped up by SeaWorld, eager to buy a new male for breeding.

Tilly's life performing (and providing sperm for the creation of 21 other captive orcas) is poignantly recalled by trainers who mostly started working at SeaWorld as idealistic, animal-loving teenagers in the 1990s. John Jett, who now teaches environmental science at university, spent four years there in the 1990s. "He has no life," he says of Tilly. "He gets beat up and he floats like a slob all day – attacked by mosquitoes by night and sunburnt by day."

In the wild, orcas swim 100 miles in a day; here, they live in relatively tiny pools. Individuals from different social groups are thrown together and fight badly, raking each other with their teeth. In small pools, there is no escape from the fighting and, as a big male, Tilly was continually attacked by naturally dominant females.

Dawn Brancheau pictured at Sea World Florida in 2009. The following year she was killed in front of horrified onlookers during one of the park's killer whale shows. Photograph: Barry Bland/Barcroft Media

Blackfish is not a balanced film, and its ending, implying we should watch whales in the wild instead, is problematic, since too many whale-watching boats have a negative impact on cetacean welfare. But Blackfish is chiefly unbalanced by SeaWorld's decision to refuse Cowperthwaite's repeated interview requests. While big corporations' standard strategy is generally to lie low (McDonald's didn't aggressively confront Morgan Spurlock over Super Size Me, for instance), SeaWorld called Blackfish "shamefully dishonest, deliberately misleading, and scientifically inaccurate" after its release, and accused the film-makers of exploiting the "tragedy" of Brancheau's death.

In a detailed rebuttal to film critics, SeaWorld argued that Blackfish wrongly asserted that captive orcas were "bullied", when fighting was natural in the wild; incorrectly portrayed SeaWorld "callously" breaking up orca families, when it tried to keep groups together; and inaccurately implied SeaWorld used punishment-based training when it only "reinforced" the "natural range of behaviours" of orcas. Most fundamentally, SeaWorld disputed the claim that Tilikum killed after being "driven crazy by his years in captivity" and argued that "all the evidence" suggested the orca was interested in Brancheau's ponytail, grabbing it and pulling her into the water where she drowned.

There is, however, credible evidence contradicting claims that Brancheau was pulled into the water by her ponytail. Former trainers view SeaWorld's theory as an attempt to attribute her death to "trainer error". After a lengthy court battle, the Occupational Safety and Health Administration fined SeaWorld for a "serious" violation of employee safety and banned it from putting trainers in the water with orcas, a ruling SeaWorld is appealing.

The marine park might be correct to say that Blackfish exaggerates the life expectancy of wild orcas versus those in captivity, but most of its rebuttals have been easily countered by the film-makers. It is indisputable that captive orcas have nowhere to escape aggression and that distressed calves are separated from their family groups. And how is it "natural" for an orca to leap out of the water to touch objects in the air, or let a human "surf" on its back?

I have more luck than Cowperthwaite in getting a response from SeaWorld. Fred Jacobs, vice-president of communications, tells me the company is unshaken by the growing musical boycott. "This appears to be an orchestrated campaign by animal rights extremists and does not reflect the reality of SeaWorld as a zoological institution, or the true nature of public opinion of marine mammal display," he says. Why does SeaWorld keep orcas in captivity? "For the same reason any zoo or aquarium displays any animal," he says. "Because it serves an invaluable educational purpose, and provides experiences that build not only awareness and appreciation for animals, but a passion to conserve them."

Nevertheless, it is still difficult to avoid the conclusion of most experts and many trainers: orcas are profoundly ill-suited to life in a tank. "Of all the places to keep killer whales in captivity," says Jett, "SeaWorld is the best – that's a pretty sad statement. Some animals can adapt to life in a captive environment, but killer whales are clearly not one of them. We can't come close to duplicating their life in the wild."

For all the outrage over Blackfish, it is business as usual at SeaWorld. After some aggressive ticket discounting, its profits in the third quarter of 2013 soared to $120m. Jett and Cowperthwaite are convinced, however, that public opinion is shifting. "I never tell people not to go to SeaWorld," says the director. "I just hope if you get anything from the film, you understand what you are seeing when an animal performs for you. Just because it's magnificent and beautiful doesn't mean it's ours."

Will Travers, of the charity Born Free, believes Blackfish will fundamentally "change public attitudes" towards orcas in the way that the 1966 film Born Free did with lions. Where musicians lead, advertisers – and the stock market – may follow. But Travers thinks it may take two decades to ban orcas in captivity: he campaigned against wild animals in circuses 19 years ago and only now is the British parliament legislating against the practice.

Former SeaWorld employees don't believe it will ever voluntarily hand over its orcas. Does SeaWorld have any plans to stop keeping these creatures in captivity? "No," says Jacobs. "In fact, a baby whale was just born in our park in San Antonio."



• Blackfish is out now on DVD and Blu-ray