Something disquieting happened at SeaWorld marine parks this year. Numbers attending the group's popular US centres between January and March dropped, from 3.5 million in 2013 to 3.05 million this year, a decline of 13%.

Nor is it hard to guess the cause, say wildlife campaigners. They see a clear link between the attendance slide and the release last year of the documentary Blackfish, which told the story of SeaWorld trainer Dawn Brancheau who was killed by Tilikum, a bull orca. The killer whale, it was also revealed, had been involved in the deaths of other individuals while in captivity.

Blackfish focuses on the distress experienced by killer whales who are depicted as complex, highly intelligent creatures which are taken from their families, kept in small pools and given psychotropic drugs to calm them and help them perform tricks that include balancing human trainers on their snouts, rotating in the water to pop music, waving their flippers and tails, and floating on their backs. The film triggered widespread public outrage against marine parks in general and a petition, signed by 1.2 million people, was handed into the California state assembly calling for a ban on killer whale shows. Earlier this month, a bill legalising the ban was put on hold for the next 12 months. Campaigners are still hopeful it will be enacted next year.

It has been an abrupt change in fortune. The cheery family charm of marine parks – institutions that have achieved worldwide popularity and become multimillion dollar industries in recent years – have taken a body blow. For their part, their managers strenuously deny that any of their animals suffer and flatly reject the idea that whales, dolphins and porpoises should no longer be kept captive.

"That argument is not based on credible, peer-reviewed science. It's based on emotion and a propaganda film," says John Reilly, the president of SeaWorld San Diego. "We believe strongly there is an inspiration benefit to people seeing [killer whales] in our park."

This last claim is outdated, campaigners respond. Modern, high-quality natural history programmes, screened on giant plasma TVs in homes, are far more likely to interest young people in wild creatures than marine park shows, they say. "Displays in which killer whales are forced to perform demeaning tricks are anything but inspirational," added Will Travers, head of the Born Free Foundation.

According to his organisation, more than 2,100 dolphins and whales are being held in captivity at 343 facilities in 63 countries around the world, with the highest numbers concentrated in Japan, China, the US and Mexico. In North America, many of these parks have become the subject of wildlife campaigns. Vancouver Aquarium is currently under intense pressure to phase out its keeping of whales and dolphins, for example, while lawmakers in New York, Texas and Florida are also considering bans on captive killer whales and other cetaceans.

In addition, it was recently reported that Richard Branson's Virgin Holidays, which sells packages to SeaWorld, had decided to begin an "engagement process" to investigate the debate around captive whales and dolphins. Branson also pledged to make his own inspection visits to marine parks, it was said.

For good measure, India last year joined Hungary, Nicaragua, Chile and many other countries in forbidding or severely restricting the keeping of whales and dolphins in captivity. For its part, the United Kingdom closed its last dolphinarium in 1993.

Wildlife campaigners say they oppose the keeping of cetaceans in captivity because these animals tend to have poor health and suffer stress-related illnesses as a result. "This is not necessarily the fault of the keepers who work with these animals and are certainly not out to mistreat them," says Lori Marino, of Emory University, Atlanta. "These parks provide good veterinary care. The problem is that cetaceans just cannot take captivity. The worst affected is the killer whale, while the beluga whale also does poorly. Bottlenose dolphins probably do best but they still die early of stress-related diseases despite being protected from predators and having food given to them every day."

A key factor is related to range. These are animals that travel and they want to travel, biologists point out. "Marine animals evolved to travel to get food," adds Marino. "It is a challenge to hunt for food and they want to be challenged that way. So it is no favour to them to throw them dead fish."

In addition, researchers point out that cetaceans have extremely sophisticated social lives which are disrupted when individual animals are caught and separated from their family groups. Killer whales have developed complex matriarchal societies in which sons and daughters live with their mothers even when they are adults. When such a family is broken up, the effect is highly stressful.

Marine parks strenuously reject suggestions that they have been involved in breaking up orca families in the wild. "SeaWorld does not collect killer whales in the wild, and has not done so in over 35 years," the company maintains in a statement, The Truth about Blackfish, that it recently put up on its website. "We do not separate killer whale moms and calves, and in the rare occurrences that we do move whales among our parks, we do so only in order to maintain a healthy social structure."

Marino disagrees, however. "The only way that these parks can get away with this sort of thing is to claim their shows have educational value or that they stimulate concern for conservation. Yet no one has required them to provide proof that they do. In fact, there is very little evidence that anything of that sort is achieved at these performances. These parks have been allowed to get away with this for decades. It is time to call them to account now."

This point was backed by Travers. "What is becoming clear is that these 'entertainments' are only achieved by keeping highly sophisticated animals in cramped artificial environments while they are controlled by chemicals. The public is beginning to understand this. That is why they are turning away."