Jimmy Savile's relationship with Stoke Mandeville Hospital has become the latest focus of a a police inquiry into allegations the former presenter abused young girls.
Savile had a "free flat" at the hospital he long supported and there is also a cafe named after him.
There have been calls to rename the cafe, as well as his charity, the Sir Jimmy Savile Stoke Mandeville Hospital Trust, since the ITV documentary Exposure: The Other Side of Jimmy Savile aired last Wednesday.
In a statement, Buckinghamshire Healthcare NHS Trust, that runs the hospital, said: "Buckinghamshire Healthcare is shocked to hear of the allegations about Jimmy Savile. We are unaware of any record or reports of inappropriate behaviour of this nature during Jimmy’s work with the Trust.
"We can confirm that the police have contacted us this week as part of their assessment exercise and we are cooperating with them fully."
Savile's headstone will be broken up and sent to landfill after it was removed late last night.
The elaborate tombstone was taken away at midnight after Savile's family requested it be removed out of "respect to public opinion".
The move came after police said they believe the "predatory sex offender" could have abused up to 25 victims over 40 years.
Savile's family said they made the decision to ensure the "dignity and sanctity" of Woodlands Cemetery in Scarborough.
The headstone, which bears the star's image and lists his accomplishments, including the epitaph "It was good while it lasted", was due to be removed at 7am today but work was brought forward to midnight to avoid unwanted attention, and out of respect for those with relatives in the graveyard.
It has now been taken to a stonemason's yard in Leeds where the inscription will be ground down and will then be broken up and sent to landfill.
Funeral director Robert Morphit, of Joseph A Hey and Son, who organised Savile's funeral and oversaw the dismantling of the headstone, said: "Yesterday afternoon the family contacted me and said they'd thought very carefully about the course of action with regard to the stone.
"They had decided that in order to protect the dignity and sanctity of this cemetery it was appropriate to remove the stone."
He said the stone was removed in three pieces and taken away on a lorry.
The grave, in which Savile was buried at an angle so he could "see" Scarborough Castle and the sea, will remain unmarked for the foreseeable future.
The prime spot was today identifiable only by several bunches of flowers on a dirt patch.
Mr Morphit said once the family comes to terms with the outcome of various investigations they will make a decision as to how it should be marked in the future.
A family spokesman said in a statement: "The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery.
"Out of respect to public opinion, to those who are buried there and to those who tend their graves and visit there, we have decided to remove it."
A number of memorials to Savile have already been removed, including an inscription on the wall at Leeds Civic Hall in recognition of his charity work, and a street sign in Scarborough. A plaque outside his home has been defaced.
Yesterday, Commander Peter Spindler, Scotland Yard's head of specialist crime investigations, said the abuse appeared to have been on a "national scale".
He said: "At this stage it is quite clear from what women are telling us that Savile was a predatory sex offender."
Scotland Yard has formally recorded eight criminal allegations against the former Top Of The Pops presenter so far in its investigation, named Operation Yewtree.
The alleged abuse involves teenage girls as young as 13 and includes two complaints of rape and six of indecent assault, with officers looking into up to 120 lines of inquiry that could lead to up to 25 victims.
Mr Spindler said allegations span four decades, the earliest dating back to 1959, and suggest Savile had a "predilection for teenage girls".
A spokesman for Scotland Yard said at least five forces - the Met, Surrey, Sussex, Northamptonshire and Jersey - are investigating allegations.
As well as claims relating to abuse at the BBC, Jersey's Haut de la Garenne children's home, and Duncroft Approved School for Girls near Staines, Surrey, police have contacted Stoke Mandeville Hospital and Leeds Royal Infirmary, where Savile did charity work.
After the inquiry, Scotland Yard will produce a joint report with the NSPCC to look for lessons that can be learned and conclusions drawn.
The NSPCC received 40 calls in the five days after the claims emerged. Of these, 24 have been referred to police or other agencies, and 17 directly relate to Savile.
There were also 21 unrelated calls to the helpline stemming from publicity over the allegations.
Chairman of the BBC Trust Lord Patten has given his backing to inquiries by police and the corporation, saying allegations against Savile could not be excused as behaviour from a time when "attitudes were different".
BBC director-general George Entwistle has also apologised to victims and said the corporation would hold its own inquiry, to follow a police probe.