According to press reports, the former Prime Minister's daughter was speaking in the green room with host Adrian Chiles and guest Jo Brand when the remark was made. It is understood that the incident was reported to the show's executive producer, and that Thatcher wrote a letter of apology. However, the BBC announced this evening that her contract on the show has not been renewed.
A BBC spokesperson said: "We will no longer be working with Carol Thatcher on The One Show."
Earlier today, Thatcher's spokesperson said that the leak of a green room conversation represented "a massive breach of trust", and added: "Carol has given the BBC an apology and as far as we are concerned we have had no apology back over this breach of confidentiality."
The journalist was crowned Queen of the Jungle in ITV's I'm A Celebrity, Get Me Out Of Here! in 2005, beating Sheree Murphy and Sid Owen to the top spot.