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After the Top Of The Pops and Jim'll Fix It presenter died in 2011 at the aged of 84, more than 450 allegations of sexual abuse emerged against him, with victims as young as five-years-old.
Coogan spoke to Sunday Brunch about the controversy surrounding new TV series The Reckoning.
He said: "I think that’s because Jimmy Savile played a trick on the entire nation so there’s a real feeling of antagonism about it.
"But you need to look at someone like that to understand how they’re able to operate and to prevent it happening again.
"If you sweep it under the carpet and just don’t talk about it anymore, then those people are destined to come back."
Writer Neil McKay revealed last year how some survivors of the Top of the Pops host's abuse wanted to attend filming and so were invited onto set.
Coogan said: "I’d go and talk to them as myself and go, 'Hi, I’m Steve, I’m not Jimmy Savile, that’s who I’m going to play today.'
"And you’re playing a role and we’re going to do it professionally, and it was so that they knew that I was someone else. So it was a tightrope, but I think we did it properly."
The Reckoning will look back at Savile's upbringing, his rise to fame and examine how his abuse went on unchecked for so many decades.
McKay has also shared that it took “a year” to convince Coogan to take on the challenging role.
News of his casting was made public in September.
Coogan said in a statement at the time: “To play Jimmy Savile was not a decision I took lightly.
“Neil McKay has written an intelligent script tackling sensitively a horrific story which, however harrowing, needs to be told.”
Responding to backlash about the series, BBC’s controller of drama commissioning Piers Wenger said the primary intention of the programme was to “give voice to the victims and to tell their stories sensitively”.
The Reckoning is set to air later this year.
Watch: The trailer for Netflix documentary Jimmy Savile: A British Horror Story