It comes after Clarkson, 62, wrote in a column earlier this week that he has dreamt of seeing Meghan, 41, paraded through the streets and publicly shamed.
His remarks prompted a backlash and have been dubbed "vile". He has since said that he was "horrified to have caused so much hurt" following the response to such.
She commented: "Someone like [Clarkson] can just say what he wants but it gets printed, that's the worst thing." She added: "We shouldn't just be able to say awful things."
Speaking to Shelagh Fogarty, 56, on her radio show earlier, Christine said that Meghan – who has spoken about wanting to take her own life in the past – might be "fragile".
Christine spoke about her late daughter Caroline, who took her own life, aged 40, almost three years ago, on the radio show. Her death came ahead of her standing trial for an alleged assault on her boyfriend Lewis Burton, now 30.
Discussing her late daughter, Christine said: "[She] had the most awful threats over things that were written in the paper." She said that "so much of it was untrue".
Christine said that she has received apologies over certain stories in the past, but further commented whilst on LBC earlier this afternoon: "It's all too easy just to apologise."
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