The report stated 22 offences happened at Stoke Mandeville, and also named Wycombe General.
BBC: Jimmy Savile scandal: Stoke Mandeville inquiry continues
The flames will then be combined at Stoke Mandeville the following day, Tuesday, 28 August.
Stoke Mandeville has set up a helpline for any worried patients or their relatives.
One woman said Savile abused her when she was a 13-year-old patient at Stoke Mandeville, Buckinghamshire.
Meanwhile, at Stoke Mandeville, a name change is already planned for the hospital's popular "Jimmy's" cafe.
The Jimmy Savile Stoke Mandeville Hospital Trust charity has closed and hospital cafe "Jimmy's" is being renamed.
She said she believed "without any doubt" other Stoke Mandeville patients must have been abused by Savile.
Stoke Mandeville set up the separate, independently-led Speaking Out investigation last year and said its inquiry was "serious and complex".
BBC: Jimmy Savile scandal: Stoke Mandeville inquiry continues
Sir Jimmy was a major fund-raiser for Stoke Mandeville Hospital, collecting millions to rebuild the National Spinal Injuries Centre (NSIC).
Savile had a flat at Stoke Mandeville hospital and he worked as a volunteer porter at Leeds General hospital for years.
Victims of Jimmy Savile's abuse at Leeds General Infirmary, Stoke Mandeville and Broadmoor hospitals are being asked to contact new helplines.
Retired Thames Valley detective John Lindsay, 71, also raised concerns about Savile abusing girls at Stoke Mandeville but said they were dismissed.
Stoke Mandeville Hospital has been contacted by police as part of an investigation into alleged abuse carried out by Sir Jimmy Savile.
Retired Thames Valley detective John Lindsay, 71, said he raised concerns about Savile abusing girls at Stoke Mandeville but they were dismissed.
Four teams scaled the highest peaks of the home countries to spark the flames which will come together at Stoke Mandeville on Tuesday.
BBC: London 2012: Four Paralympic flames kindled around the UK
Stoke Mandeville Hospital has said it is continuing its inquiry into Jimmy Savile as a police report revealed 22 offences had occurred there.
BBC: Jimmy Savile scandal: Stoke Mandeville inquiry continues
This involved allegations that the veteran broadcaster had sexually assaulted two teenage girls at Duncroft Approved School and a girl at Stoke Mandeville Hospital.
BBC: Surrey Police orders review of child sex investigations
Dr Patrick Kluger, a spinal injury expert who works at Stoke Mandeville Hospital, said the robot was one of several techniques currently being developed.
The cafe at Stoke Mandeville Hospital in Aylesbury was opened by Savile in 2005 following his years of fundraising for the spinal injuries unit.
Phyllis Collins was sent from Stoke Mandeville hospital to her home in Aylesbury by taxi at 02:00 GMT on 12 January without her family's knowledge.
He was sent for rehabilitation at Stoke Mandeville Hospital in Buckinghamshire.
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During their investigation two more allegations emerged - the first that in about 1973 Savile had sexually assaulted a girl aged about 14 outside Stoke Mandeville Hospital.
But police are investigating claims he abused up to 300 young people, including at three hospitals which he raised funds for: Broadmoor, Stoke Mandeville Hospital and Leeds General Infirmary.
The decision was made after allegations made by Caroline Moore, now 53, that Savile sexually assaulted her in a Stoke Mandeville corridor in 1971, when she was a 13-year-old patient.
The Paralympic relay involves four flames being lit in London, Edinburgh, Cardiff and Belfast which are united in the Paralympic Torch at the national centre for disability sport in Stoke Mandeville, Buckinghamshire.
Sylvia Nichol, a trustee of The Jimmy Savile Stoke Mandeville Hospital Trust, told BBC Three Counties she had known Savile for many years and had found it hard to come to terms with the allegations against him.
Asked if allegations related to any institutions other than those mentioned in previous claims - the BBC, Jersey children's home Haut de la Garenne, or Duncroft Approved School in Staines, Surrey - he said he had contacted Stoke Mandeville Hospital and Leeds Royal Infirmary.
Liz Dux, from law firm Russell, Jones and Walker, said letters had been sent to the Savile estate, Stoke Mandeville Hospital, Broadmoor, Leeds General Infirmary and the BBC saying 20 clients who claim they were abused by the late presenter are considering legal action.
BBC: Broadcaster backs BBC against Jimmy Savile 'witch-hunt'
Although the first Paralympics were held in Rome in 1960, they were inspired by the Stoke Mandeville Games - a sports contest for British World War II veterans with spinal cord injuries that was organised by Dr Ludwig Guttmann of Stoke Mandeville Hospital in 1948.
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