Buxton argued that humans no longer need to eat fatty and sugary foods to survive because there are so many easily accessible healthy options and alternatives.
She said: "We're pre-destined from our caveman times to get as much sugar and fat whenever we can, wherever we find it, because that's what we had to do in caveman times for survival. We don't need to do that anymore.
"Cakes and sugar are everywhere and so it's my job as a parent to govern my child, they can't self govern themselves, so that's why I have to stop them having sugar."
The show was debating the issue following the news that one in 10 UK parents don't let their children have birthday cake at parties to prevent them becoming overweight.
uxton, whose children range in age from 10, said she rules out giving her young children treats altogether, so that they won't become addicted.
She said: "Sugar has the same effect on the brain as cocaine, so once [they] have one they go crazy, they're running around, they want more, and then another hit and another hit.
"You're better off not having any, and then having something that's better for you."
But viewers took to Twitter to question her strict stance, with many insisting she was denying her children important childhood experiences.
One tweeted: "Oh god heard it all now with this woman. Leave people be to parent their own children. Have a cake and enjoy life. God if that was my mother!! What a boring woman."
"I think this is going over the top now," another posted.
A third said: "Omg really??? This is getting stupid!!! How about sweets go back to being a treat like it was when i grew up not a everyday diet!!! That's the excitement of going to party as a kid the cakes and sweets, didn't have them everyday at home."
"Food is not problem, lack of exercise is!!!!! Let kids be kids!!!!" another agreed.
Speaking opposite Buxton in the debate was parenting expert Amanda Jenner, who argued that children should be allowed to have treats.
Jenner, herself a mother of three, admitted she does limit her own children's sugar intake by banning fizzy drinks in her house, but said enjoying birthday parties is an important part of childhood.
She said: "I'm a great believer in that kids have got to be kids - going to that birthday party and bringing out that cake is all about growing up.
"Yes in moderation - I'm not saying give them 20 cakes a day or anything - but you've got to give them the odd treat, children like treats. As a kid you look forward to that, so if you know they've got a party at the weekend then cut the sugar out during the week."
