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LONDON — Scotland Yard and Britain’s leading child-welfare group drew a picture of more than 200 cases of sexual abuse of victims as young as 8 by the BBC host Jimmy Savile in a report released Friday, and prosecutors admitted for the first time that “shortcomings” in interviewing some victims allowed Savile to escape prosecution before his death at age 84 in 2011.

The report, jointly written by the police and the National Society for the Prevention of Cruelty to Children, depicted a pattern of abuse in broadcast studios, hospitals, homes for the mentally disabled and other places of care for the vulnerable. It documented 23 offenses committed at the BBC’s television center in London during Savile’s 40 years there, including one assault during the taping of the last episode of his “Top of the Pops” show in 2006, when the performer was nearing 80.

Only one location, Stoke Mandeville Hospital, about 40 miles northwest of London, with 24 attacks, was the site of more offenses than the BBC. Savile maintained living quarters and an office at the hospital and was free to roam it as an honorary porter after raising millions of pounds with a charitable appeal for its spinal-injuries unit.

The report, which referred to the entertainer as James Wilson Vincent Savile, said police had received more than 450 individual complaints, ranging from groping to forced oral sex and rape, with many of the accusations still awaiting police investigation. It gave a breakdown showing that most victims, 73 percent, were younger than 18, with the largest group 13 to 16 years old. Overall, the report said, 82 percent of the victims were female.

The offenses spanned from 1955 to 2009, the report said, with the peak from 1966 to 1976, when Savile was at the pinnacle of his popularity, drawing millions to his prime-time shows.

The report describes a “prolific, predatory sex offender” whose celebrity unlocked the doors of institutions across Britain, from hospitals where he served as a charity fundraiser to schools whose pupils eagerly watched his television programs — and even to the prime minister’s country house, where he dined with Margaret Thatcher.

The crisis prompted the resignation of BBC’s director general, George Entwistle; a shake-up in its news division; and an inquiry that reported last month that lax leadership and “rigid management chains” had left the corporation “completely incapable” of dealing with Savile’s behavior.

The scandal has also tainted the National Health Service,

Savile was long celebrated as a zany national treasure, with a near-saintly commitment to charitable work with children; he was knighted by Pope John Paul II and Queen Elizabeth II, and one of the report’s central conclusions is that he matched the huge following he built across Britain, especially among children, with a chilling ability to work his way into the confidence of his victims.

He then escaped the consequences of his abuse on the strength of his soaring popularity and the victims’ reluctance to pit their accusations against his seemingly impregnable renown, the report said.

“It could be said that he groomed a nation,” said Cmdr. Peter Spindler, the Scotland Yard officer who led the police inquiry. “He was hiding in plain sight, and none of us was able to do anything about it.”

He added, “This whole sordid affair has demonstrated the true consequences of what happens when vulnerability collides with power.”

The report said the offenses ranged from “opportunistic touching over or under clothing,” including groping young fans during breaks in the filming of his prime-time shows, “Top of the Pops” and “Jim’ll Fix It,” at BBC studios in London, to dozens of cases of “coercion, violence and rape.” The most serious offenses, described in the report as involving rape or penetration, involved 26 females and eight males.

“The formal recording of allegations of crime on this scale is, to the best of our knowledge, unprecedented in the U.K.,” the report said.

In the welter of apologies prompted from organizations named in the report as having failed to stop Savile, one that stood out was from the Crown Prosecution Service, which issued a statement acknowledging that three victims who accused Savile of abuse in 2009 were not taken seriously enough.

Keir Starmer, the service’s director, said an “unjustified” degree of caution “often resulted in sexual offenses being subjected to a different, and, in reality, more rigorous test than that applied to other crimes.” New rules would require prosecutors to make greater efforts to build a case around the allegations of abuse victims, Starmer said.

The report suggested prosecutors were not alone in their inaction.

“Why did it happen and why was it not noticed and stopped by police, health, education or social-services professionals, people at the BBC or other media, parents or … politicians, or even ‘society in general’?” the report asked.