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.
More top news
The United States' newest armed force had a very familiar-looking uniform for some very unfamiliar frontiers.
KPMG has been appointed and will continue to seek a buyer for the 139-year-old business.
His comments followed the announcement of £620 million in financing to support projects and UK exports to Africa.