Thatcher, the daughter of Britain's Conservative former Prime Minister Margaret Thatcher, compared a player in the Australian Open, thought to be Frenchman Gael Monfils, to the golliwog that once appeared on jars of Robinson's jam.
Thatcher herself has reacted with bemusement at the furore sparked by her comment, which was made off air -- backstage in the show's green room.
According to a report in the Daily Mirror, her comment was overheard by at least a dozen people, including the show's host Adrian Chiles, to whom it was reportedly made, and comedian Jo Brand.
Quoted in the paper, Thatcher said: "I'm completely baffled by the fuss that's being made about this. I really am.
"It was a private conversation between people in the communications business and I've nothing more to say on the matter."
Chiles is said to have been "very shocked" by the comment, which led BBC executives to write to Thatcher demanding an apology.
The corporation originally said in a statement: "The BBC considers any language of a racist nature wholly unacceptable.
"We have raised the issue with the individual concerned and are discussing it as a matter of urgency."
Thatcher, who has spent three years reporting for 'The One Show', apparently apologised privately to the producer of the show, but has refused to make an official apology.
The BBC has since said that it would no longer work with Thatcher on the programme.
Her own spokeswoman said: "This was a conversation between Adrian and Carol and the comment was meant as a joke.
"It's disgusting that we've had a leak of private conversations in the green room. The BBC has more leaks than Thames Water."
Thatcher shot to fame when she became the 2005 winner of ITV's reality show 'I'm A Celebrity... Get Me Out Of Here!'
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