In her latest Mail on Sunday article, Jones explained why she dislikes the BBC presenter, criticising her dress sense and passion for horse racing.
Jones said that she was not a fan of Balding, because "she stands on the turf at Aintree or Goodwood in her cheap hat and shoes, wielding her microphone, and she does not criticise the use of the whip by jockeys, or collapse in tears and rage when yet another horse has broken its neck".
She also accused her of supporting "without question, a sport that is intrinsically barbaric", and of having a "sense of superiority".
Jones also attacked Balding's recent statement that "warmth, humour, intelligence, doing your homework" were more important than a woman's looks on air.
The columnist said that Balding's comments meant "that the rest of us who bother to shop in Prada and have facelifts cannot possibly be as 'good' as she is, nor be as nice or as worthy".
Balding reacted to the piece on Twitter, stating that she would not accept an interview with her.
She tweeted: "Please don't turn today into a Liz Jones hatefest. I'm not upset at all. She has merely justified my choice not to be interviewed by her."
Liz Jones was criticised by Phillip Schofield last year, after she wrote an article about Holly Willoughby in which she described her as "anti-feminist".
He said at the time: "I swear there can be no greater force against all womankind than Liz Jones. She is inconsistent, bitter, nasty and unhinged."
Clare Balding was widely praised for her coverage of the London 2012 Olympics for the BBC, and began hosting Britain's Brightest earlier this month.
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