In the article which has been removed by the newspaper's website, Clarkson wrote that he has been "dreaming of the day when she is made to parade naked through the streets of every town in Britain while crowds chant, 'Shame!' and throw lumps of excrement at her", claiming "everyone who's my age thinks the same way".
"I hate her", the former Top Gear host had previously written. "Not like I hate Nicola Sturgeon or Rose West. I hate her on a cellular level".
"But what makes me despair," he added, "is that younger people, especially girls, think she's pretty cool".
Following this, Clarkson has received strong backlash over the piece, from the likes of Carol Voderman, Jason Manford and his daughter Emily.
"My views are and have always been clear when it comes to misogyny, bullying and the treatment of women by the media", Emily wrote on her Instagram account. "I want to make it very clear that I stand against everything that my dad wrote about Meghan Markle and I remain in support of those that are targeted with online hatred".
"If you can defend Clarkson in this then please don't reply to me, just unfollow and block and move on. We are never going to agree", comedian Jason Manford said.
Following the severe backlash, Who Wants To Be A Millionaire host Jeremy Clarkson responded to the flack, calling the comments "totally unacceptable".
"Oh dear. I've rather put my foot in it. In a column I wrote about Meghan, I made a clumsy reference to a scene in Game of Thrones and this has gone down badly with a great many people. I'm horrified to have caused so much hurt and I shall be more careful in future", Clarkson wrote.
"In light of Jeremy Clarkson's tweet he has asked us to take last week's column down", the Irish Sun also announced.
