Claims have emerged that Savile groped young patients at Stoke Mandeville Hospital in Buckinghamshire, where he was a volunteer fundraiser, while one woman has claimed she saw him molest a brain-damaged hospital patient at Leeds General Hospital.
The new allegations come as Tayside police said a second Scot claiming to be a victim of Savile will be interviewed by detectives from Scotland Yard in London, which is dealing with the flood of complaints against him.
Earlier this week, Caroline Moore, from Clarkston, in East Renfrewshire, claimed Saville obscenely kissed her when she was 13.
The 53-year-old, who is paralysed from the neck down, was a patient at Stoke Mandeville.
Nurses at Stoke Mandeville are understood to have dreaded Savile's visits, and would tell children to stay in bed and pretend to be asleep when he came round.
Former patient Rebecca Owen said she overheard nurses talking in a way that suggested he also targeted them. She said: "There was some ironic chatter about who would be the lucky one to go off to his room."
A spokesman for Buck-inghamshire Healthcare NHS Trust, which runs Stoke Mandeville, said it was fully supporting police inquiries.
A spokesman for Leeds Teaching Hospitals NHS Trust said it had contacted police.