Simon Bass, from the Churches Child Protection Advisory Service (CCPAS), was speaking after the release of the Dame Janet Smith report (below) on the former DJs' sexual crimes - and how the BBC responded to them.
The report found Savile raped and sexually assaulted 72 people while working for the BBC since 1959, while Stuart Hall sexually assaulted 21 people since the 1960s.
Jimmy Savile died in 2011 before any charges could be brought against him, while Stuart Hall was jailed in 2013 after admitting indecently assaulting 13 girls, the youngest being nine years old.
BBC staff missed five opportunities to expose what they were doing because of a culture of "fear and reverence" towards its talent which left them unchallenged and victims not believed.
There was also a culture of treating victims claiming they were abused by the DJs as nuisances.
Simon Bass, from CCPAS, told Premier: "There needs to be a change clearly of culture in terms of making it more open, which means that everyone should have safeguarding training.
"It would appear that the executive management at the BBC were not made aware, and the question has to be: why?
"CCPAS has been calling for mandatory reporting for some time now, because we simply don't have a duty to report abuse.
"I hope that this is a wake-up call."
The inquiry did exonerate the corporation as a whole, as it found no evidence that senior executives knew about Hall or Savile's abuse.
The BBC has apologised to the victims and has admitted it failed them. It has also pledged to fully review its safeguarding practices and policies - something it has been doing ever since allegations against Hall and Savile came to light.
Listen to Premier's Alex Williams speaking to Simon Bass on the News Hour:
