Others stayed silent because they were convinced they would not be believed as the radio and TV presenter was such a powerful and influential character.
Some victims were even told they were “lucky someone like Savile had paid them attention”, according to the NSPCC report.
A significant number of the men and women interviewed have still not confided in friends and family about the abuse, the children’s charity said.
Savile died aged 84 in October 2011 - a year before allegations that he had sexually abused children were broadcast in an ITV documentary.
The revelations about the former BBC presenter of Top Of The Pops and Jim’ll Fix It prompted hundreds of victims to come forward with claims that they were attacked at BBC premises or in other institutions, including hospitals.
According to the report, Would They Actually Have Believed Me?, some of the victims, who were aged between eight and 26 when Savile assaulted them, told hospital staff, who dismissed their claims.
One of the 26 victims interviewed by NSPCC counsellors went to the police but no action was taken. The vast majority were children when they were abused but four were adults.
The NSPCC said the research, which was commissioned by Her Majesty’s Inspectorate of Constabulary, highlighted the “devastating scars” that victims had suffered from the abuse, with some turning to drink and drugs to cope. Others have suffered mental illness, poor relationships or contemplated suicide, it said.
Peter Watt, the NSPCC’s director of national services, said: “The responses these victims received when they first revealed Savile’s sickening crimes makes heart-rending reading.
“They were ignored, dismissed, not believed, laughed at and, astonishingly, told in some cases they should feel lucky he had paid them attention.
“Half a century on, the world finally discovered just how dreadful his crimes were - something these men and women had known all that time but felt powerless to do anything about.
“The anger, frustration and sheer helplessness of the situation obviously damaged their lives in various ways. But they showed true courage in coming forward once more to talk about their experiences and hopefully they can now start to put the terrible trauma behind them.”
The report found that, when Savile’s sex crimes became public knowledge at the end of 2012, some victims suffered flashbacks and felt physically sick when they saw pictures of him.
Extensive media coverage encouraged them to come forward and report the crimes, the NSPCC said.
Three-quarters of victims interviewed did not realise as children that they had been sexually abused by the late DJ, the report found.
Some of those interviewed said they were aware of wrongdoing but felt helpless, ashamed or intimidated by Savile’s fame, with some believing the abuse had to be reported by an adult.
“I never thought I could go to the police on my own,” one victim said. “Children’s minds work completely differently, don’t they?”
According to the report, victims had “largely positive experiences” when they finally went to the police after Scotland Yard launched Operation Yewtree in the wake of the TV expose about Savile.
But they wanted to see improvements, including new ways to report sexual abuse and additional specialist training for officers receiving and investigating allegations to ensure they fully appreciate the long-term emotional impact of the crime, the NSPCC said.
Her Majesty’s Inspector Drusilla Sharpling said: “I am deeply grateful to the victims who contributed to this powerful and moving report.
“It vividly portrays the pain and anguish suffered by Savile’s victims, which was often made worse by the way they were treated.
“Despite the difficulties they have faced, victims have highlighted important ways in which police responses can be improved. We owe it to them to make sure that the police service responds positively and ensures victims are supported, listened to and treated with compassion.”
‘Good guy’ Savile
A key reason for not reporting the abuse was an “overwhelming belief” from victims that they would not have been believed at the time, the NSPCC said.
“Jimmy Savile was a powerful and influential adult, who was seen as a ‘charitable, good guy’ raising a lot of money for charity,” the report said.
“This led to feelings of hopelessness and inferiority in his victims, who felt there was no way that their word would have been believed over his.”
Crime Prevention Minister Norman Baker said: “It is encouraging to hear that these victims felt the response from police was largely supportive.
“While we can never right the horrific wrongs committed against these people, we must ensure we do all we can to protect the most vulnerable in our society from becoming victims again in the future.
“This is why I am leading a national group of experts to tackle sexual violence against children and vulnerable people.
“The group will be publishing a new action plan in the spring so that the most robust safeguards are in place to protect the children and vulnerable adults of today and the future.”