Jeremy Everard demanded that his daughter's killer look at him as he delivered an emotional victim impact statement in court.
He told Couzens: "I can never forgive you for what you have done, for taking Sarah away from us.
"You burnt our daughter's body - you further tortured us - so that we could not see her again."
Couzens appeared to shake in the dock as Mr Everard went on: "You murdered our daughter and forever broke the hearts of her mother, father, brother, sister, family and her friends.
"Sarah had so much to look forward to and because of you this has now gone forever."
Ms Everard's sister Katie Everard described Couzens as a "monster".
Weeping as she read her statement, she said: "You used your warrant card to trick my sister into your car. She sat in a car handcuffed for hours.
"What could she have thought she had done wrong? What lies did you tell her? When did she realise that she wasn't going to survive the night?
"My only hope is that she was in a state of shock and that she wasn't aware of the disgusting things being done to her by a monster. When you forced yourself upon her and raped her."
Sarah Everard's mother Susan said she is "haunted" by the horror of her daughter's murder.
Reading a statement at the Old Bailey, she said: "Sarah died in horrendous circumstances. I am tormented at the thought of what she endured.
"Sarah was handcuffed, unable to defend herself, and there was no one to rescue her. She spent the last hours on this earth with the very worst of humanity.
"She lost her life because Wayne Couzens wanted to satisfy his perverted desires. It is a ridiculous reason. It is nonsensical. How could he value a human life so cheaply?
"I am incandescent with rage at the thought of it. He treated my daughter as if she was nothing and disposed of her as if she was rubbish."
Mrs Everard said she was "repulsed" by the thought of what Couzens did.
She added: "I am outraged that he masqueraded as a policeman in order to get what he wanted."
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