Other important medical projects could also be hit, according to Dr Roger Bodley, a consultant at Stoke Mandeville Hospital in Buckinghamshire and a trustee of the Sir Jimmy Savile Charitable Trust.
Savile raised in excess of £40 million for Stoke Mandeville over 25 years.
Mr Bodley's warning came as Surrey Police said the host of the BBC's Jim'll Fix It was questioned over allegations of child sex abuse in 2007, four years before he died in October last year, aged 84.
The force said an individual was interviewed over offences alleged to have occurred at a children's home in the 1970s. It added that the Crown Prosecution Service said there was insufficient evidence for further action.
Mr Bodley had been alerted to an ITV documentary to be shown tomorrow, which will feature allegations of sexual abuse against under-age teenage girls by the entertainer.
Admitting he did not know if there was any truth in the allegations, Mr Bodley added: "The definite fact that can be stated is his two charitable trusts have already supported several very effective projects in Leeds University and The National Spinal Injuries Centre, Stoke Mandeville Hospital, as well as being about to support the conversion of his cottage in Glencoe for use by the disabled –projects that are overwhelmingly beneficial to the community but which will be gravely curtailed by adverse sensationalist publicity that we believe cannot be proven.
"Certainly the truth must be paramount. The good that is threatened is definite but any adverse allegations must be backed up by evidence."
Although there had been previous allegations, Savile was never charged with any abuse offences, and his family and friends say they are disgusted and appalled by the prospect of his memory being besmirched.
Savile was a popular figure in the Highlands and a frequent visitor since he bought a cottage in Glencoe in 1998 for a reported £125,000.
But one woman who knew him, but asked not to be named, said she had a different perspective: "I had a close friend for many years who sadly has since died. She had known Jimmy Savile in the north of England and told me a story about him when she was a young girl.
"She didn't tell me with any great rancour at all. It was more a matter-of-fact thing; that this is what Jimmy Savile did.
"I don't think it ever went beyond him being far too touchy feely. He didn't have sex with her or anything close to it. But it was certainly highly inappropriate behaviour for any man towards a girl who was probably about 10 or 11 at the time."
However, Scots mountaineer Hamish MacInnes, who was a friend of Savile's and once owned the cottage in Glencoe the DJ bought, spoke in his defence.
He said: "These allegations really don't ring true to me. I knew Jim pretty well and we had long talks. So I have serious doubts about all this."
Drew McFarlane-Slack, a former councillor for the Ballachulish and Glencoe area, said: "He was seen as something of a hero in Lochaber. I doubt many people here will believe what is now being said about him."
Meanwhile, Paul Gambaccini said his former Radio 1 colleague played tabloid newspapers "like a Stradivarius" violin to keep any allegations of impropriety quiet.
Gambaccini told ITV1's Daybreak he had been waiting 30 years for such stories to come out. He said Savile was about to be exposed by one newspaper, but gave an interview to a rival tabloid that had the effect of stopping it.