June Thornton, a patient at the LGI in the 1970s, told BBC Look North she had witnessed Savile come into her ward and abuse a female patient who was incapacitated.
Lead signatory Mark Darowski, a children's intensive care specialist at the LGI, said if paediatric heart surgery in Leeds did end it would mean a three-fold rise in journey times for children needing urgent treatment.
The petition against the proposals, containing signatures from specialists across Yorkshire and the Humber, was handed to members of the Independent Reconfiguration Panel while on a fact-finding visit to the LGI.