Dr Sue Proctor, who led the investigation into Savile's abuse at the LGI has told how abuse by Jimmy Savile took place in wards, corridors and offices.
She said that reports were made but none passed on to senior staff.
She blamed "organisational failures" - including a lack of security and poorly supported and used systems for complaints:
The family of Jimmy Savile say they are devastated by the findings of reports into the disgraced TV star's behaviour at hospitals across the UK.
We are truly devastated by this report and its findings. It is hard to believe the extent of what has happened. It seems that the Jimmy Savile we knew, and the one the public knew, is a completely different person to the one described in this report.
The Broadmoor Hospital report into Jimmy Savile found there were clear failings in the way access to the hospital was controlled during the time he was connected to the institution.
- A closed and introspective institutional culture, encouraging a custodial approach to 'inmates' and permitting instances or harsh treatment
- A 'notable absence of written polices and procedures' over most of the time Savile was involved with the hospital
- Savile had keys allowing him unrestricted access to ward areas within the security perimeter
- Sexual relationships between staff and patients were tolerated in what was a "clear, repeated failure of safeguarding standards".
Jimmy Savile claimed to more than one person that some of his elaborate rings were made using the glass eyes of dead bodies from his "friends" at Leeds General Infirmary, Dr Sue Proctor, lead investigator at LGI, said.
The late entertainer, who had spoken of his interest in dead bodies in various media interviews, told a student nurse that he committed sex acts on the bodies in the hospital's mortuary when it was "quiet".
Jimmy Savile's activities in the mortuary at Leeds are particularly harrowing.
He told one person he had "committed sex acts" with bodies there.
An investigation into Jimmy Savile's conduct at Broadmoor Hospital found that as well as discouraging complaints,** **sexual relationships between staff and patients were tolerated in what was a "clear, repeated failure of safeguarding standards".
The report noted that Savile would watch as female patients undressed for baths in the wards, and at other times looked through doorways while making inappropriate comments.
Savile's "often flamboyantly inappropriate" attitude towards women was see as part of his public act, "just Jimmy", the report found.
A report by Broadmoor Hospital into abuse undertaken by its former patron Jimmy Savile described the late entertainer as an "adept manipulator of people".
It said as well as having his own keys and accommodation on the premises, he used his influence at the hospital to have a close associate appointed as general manager, who remained in charge of the institution for eight years.
Savile "used this connection and the 'friends in high places' he boasted of" to threaten staff with dismissal if they complained about his behaviour, the report said.
While Savile's "unconventional and promiscuous lifestyle" was apparent at the time, the hospital said there was no evidence that officials "knew anything of the very much darker side that has since become evident."
Findings of the investigations into Jimmy Savile's abuse of patients and staff at hospitals are "truly awful", NHS chiefs have said.
"The abusive behaviour of Jimmy Savile on NHS premises described in today's reports is truly awful," a joint statement between the heads of NHS England, the Trust Development Authority, Care Quality Commission and Monitor said.
"Our sympathy is with all the victims and we acknowledge their bravery in coming forward to talk to the investigations."
Both current chief executives of Leeds Teaching Hospitals NHS Trust and West London Mental Health NHS Trust, which covers Broadmoor, have apologised to victims.
Jimmy Savile had a friend installed as general manager at Broadwater Hospital while he abused at least five individuals at the hospital, an investigation has found.
ITV News Political Correspondent Carl Dinnen tweeted:
Jimmy Savile had a friend installed as General Manager at Broadmoor Hospital, investigation finds.