Jimmy Savile's victims also include parents, friends and health professionals traumatised by guilt a charity has said.
A West Yorkshire police officer who knew Jimmy Savile has won £60,000 libel damages over claims that he was a pervert.
The trust which runs Leeds General Infirmary where Jimmy Savile carried out years of abuse says the report is "profoundly shocking".
Health Secretary Jeremy Hunt has apologised on behalf of the government and NHS for letting down the victims of Jimmy Savile, after a series of investigations found Savile had subjected patients in hospitals to "sickening" sexual abuse.
"Today I want to apologise on behalf of the Government and the NHS to all the victims who were abused by Savile in NHS-run institutions," Mr Hunt told MPs.
"We let them down badly and however long ago it may have been, many of them are still reliving the pain they went through.
"If we cannot undo the past, I hope that honesty and transparency about what happened can at least alleviate some of the suffering, it's the least we owe them."
A woman who was sexually assaulted in a hospital basement by Jimmy Savile when she was a teenage patient said she feels "betrayed" by Leeds Teaching Hospitals NHS Trust.
The now 57-year-old was abused by the disgraced entertainer in Leeds General Infirmary in 1973, when he was volunteering as a porter at the hospital.
She said wants an apology from the trust and reassurances such abuse can never happen again.
The woman, who was an in-patient at the time, said that she had attempted to report the abuse to nurses, but they laughed off her complaints.
"In my opinion, the hospital let me down," she told the Press Association. "They let me down by allowing that to happen, but they also let me down two years ago when they didn't acknowledge it had happened."
"The fact that they just didn't even reply to my emails until I really bombarded them, and then they did. That's like I was betrayed twice, let down twice, the fact they didn't believe me."
A nurse at Whitby Hospital claims Jimmy Savile inappropriately touched her during a visit in the 1960s. The claim has been investigated by York Teaching Hospital NHS Foundation Trust, one of 28 Trusts publishing the findings of Savile investigations.
The investigation began after a former member of staff at the Whitby Memorial Hospital, which was demolished in the 1970s, made a complaint. Savile is alleged to have 'put his arms around her and touched her inappropriately', though not in a sexual way, and made an inappropriate comment.
She claimed Savile visited the hospital occasionally, sometimes alone and sometimes with a driver and was very 'touchy feely' and used to 'paw you'. She didn't make a complaint at the time but said she told him not to behave inappropriately.
– Mike Proctor, Deputy Chief Executive, York Teaching Hospital NHS Foundation Trust
It is important the NHS plays its part in investigating allegations relating to Jimmy Savile and we took our duty to do this seriously. Our investigation centred on a single allegation at Whitby Hospital, which was an isolated incident that does not appear to have caused long term harm to the individual concerned. Our investigation also highlighted that, 50 years ago, society was very different and we now have much greater awareness of the dangers to vulnerable people, with systems and processes in place to better protect them."
- Read more on the Savile investigations here.
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.
– Savile family statement
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."