The Vienna-born grandson of Freud, the founder of psychoanalysis, is believed to have abused two girls between the late 1940s and 1970s.
The revelations emerged in a documentary titled 'Exposure: Abused and Betrayed - A Life Sentence', to be broadcast on the UK's ITV channel.
"I just want to clear things up before I die...I want to die clean. Having been so hard on myself, trying to destroy myself so many times, you can't bury the truth forever, it needs to be heard," said Sylvia Woosley, one of the victims who first met Clement when she was 10 and was sent to live with him at 14 after her parents' marriage broke up.
A second woman, who wants to remain anonymous, claimed Clement abused her as a child and raped her when she was 18.
Clement died at his home on 15 April 2009, nine days before his 85th birthday.
Clement's widow Jill Freud said she was "deeply saddened" after her children viewed the documentary on her behalf before telecast.
In a statement, the 89-year-old said: "This is a very sad day for me. I was married to Clement for 58 years and loved him dearly.
A Liberal MP from 1973 to 1987, Clement was knighted by the Queen in 1987.
Besides becoming a celebrity chef, he contributed to BBC Radio 4's 'Just A Minute' show for more than 30 years.
He was best known in the UK for eccentric pet food commercials with "Henry the dog", which kick-started his long career as a television and radio personality.
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