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In a wide ranging interview on the Andrew Marr Show, Mr Stevens described obesity as the "new smoking", urging parents, schools and the food industry to do more to tackle it.
He pointed to a string of Saturday newspaper reports warning that obesity will soon overtake smoking as the leading cause of cancer.
Mr Stevens said one in five cancer deaths was now caused by obesity, adding that the food industry had a "huge responsibility here".
He said: "I do think we are going to need reformulation to take sugar out of foods in the same way that has successfully happened with salt over the last several years. I think responsible retailers, food producers, can smell the coffee here.
"They can see that public attitudes are changing and they are going to need to take action because we can see that if that doesn't happen, then in effect what we are doing is a slow burn of food poisoning through all of this sugar that then goes on to cause cancer, diabetes, heart disease.
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