"The food industry has proved itself incapable of acting in a socially responsible way," Sustain spokesman Charlie Powell told the Daily Telegraph.
"For the sake of children's health, statutory controls are urgently required."
Though directed at the government, the government did not respond warmly, the Telegraph said Wednesday.
Culture Secretary Tessa Jowell rejected the call, saying she was sceptical it would help tackle the problem of obesity.
"We are getting fatter because we are less active," she said.
Among the groups backing the advertising ban are the British Allergy Foundation, British Dental Association, British Dietetic Association, British Heart Foundation, Children's Society, Friends of the Earth and the National Consumer Council.