LONDON — Scotland Yard and Britain’s leading child welfare group drew a horrific 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 on Friday, and prosecutors admitted for the first time that “shortcomings” in interviewing some of the victims allowed Mr. Savile to escape prosecution before his death at the age of 84 in 2011.

The 37-page report, jointly written by the police and the welfare group, 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 Mr. 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 was. Mr. 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 in criminal fashion as James Wilson Vincent Savile, said the police had received more than 450 individual complaints against Mr. Savile, ranging from groping to forced oral sex and rape, with many of the allegations still awaiting police investigation. It gave a breakdown showing that the preponderance of the victims, 73 percent, were younger than 18, with the largest group 13 to 16 years old. Over all, the report said, 82 percent of the victims were female.