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Jeremy Clarkson's daughter says she "stands against everything" he wrote about the Duchess of Sussex in a controversial column for the Sun.
The broadcaster said he "hated [Meghan] on a cellular level" in an article published in the newspaper on Friday.
His comments were widely criticised on social media over the weekend.
On Sunday, Emily Clarkson said: "I want to make it very clear that I stand against everything my dad wrote about Meghan Markle."
Ipso, the independent press standards organisation, confirmed it has received complaints regarding the column.
The Sun told BBC News it doesn't have anything further to add. Jeremy Clarkson's representative has also been contacted.
Writing in his original column, Clarkson said: "I hate her [Meghan] on a cellular level.
"At night, I'm unable to sleep as I lie there, grinding my teeth and dreaming of the day when she is made to parade naked through the streets of every town in Britain while the crowds chant 'Shame!' and throw lumps of excrement at her.
"Everyone who's my age thinks the same way," he added. "But what makes me despair is that younger people, especially girls, think she's pretty cool. They think she was a prisoner of Buckingham Palace, forced to talk about nothing but embroidery and kittens."
His column followed the release of the last three episodes of Netflix's docuseries Harry & Meghan on Thursday.
Posting on her Instagram page on Sunday, podcast host Emily Clarkson said she supports those "targeted with online hatred".
"My views are and have always been clear when it comes to misogyny, bullying and the treatment of women by the media," she wrote.
"I want to make it very clear that I stand against everything my dad wrote about Meghan Markle."
In last week's final instalment of their Netflix series, the Duke and Duchess of Sussex spoke about the mental health impact the tabloid media has on them.
The couple argued that Meghan's biracial heritage was often an underlying factor in what they described as a relentless tabloid campaign against her, and in racist abuse she suffered online.
Emily Clarkson has previously criticised the media for being "poisonously misogynistic" in its coverage of the Duchess, as well as other women.
Other high-profile Twitter users who criticised Clarkson's column included Carol Vorderman, Edith Bowman, and John Bishop.
NO Jeremy Clarkson. Not on any level, in any circumstance, is it ok to write this stuff about any woman & absolutely NO to "everyone who's my age thinks the same"
No no no. We absolutely do NOT think the same.
Listen to the noise Jeremy. The crowds are chanting "shame on YOU" pic.twitter.com/OzCt9lHG16
The BBC is not responsible for the content of external sites.View original tweet on Twitter
But Alex Phillips, a journalist and former Brexit Party MEP, defended Clarkson, telling ITV's Good Morning Britain she believed he is "deliberately pushing boundaries to be offensive".
She said he's "not there to be taken seriously" and "his word is there to be found funny, and it always has been".
Phillips added: "Taking something that happened in Game of Thrones, one of the most widely-watched TV series... Does he mean it? Of course he doesn't mean it."
Jeremy Clarkson is the star of Amazon Prime Video series The Grand Tour and Clarkson's Farm and also hosts Who Wants To Be A Millionaire? for ITV.