Boyd Swinburn, the university's professor of population health and global nutrition, said the strong support for a clampdown on junk-food promotion to kids was a call for the Government to act.
"Clearly the public are very supportive of the Government taking a much stronger lead in protecting children and supporting parents by restricting unhealthy food marketing that targets children."
Health Minister Jonathan Coleman was unavailable for comment.
Professor Swinburn said there were no Government restrictions on marketing to children and only a variety of self-regulated industry codes. Self-regulation was ineffective.
The code on TV advertising did not recognise that for many children the main viewing time was prime time, not the protected children's times.
Research published by his colleagues in 2006 found that children who watched the most television were more likely to be higher consumers of the foods most commonly advertised on TV - sugary drinks, sweets, snacks and fast food.
The Food and Grocery Council's chief executive, Katherine Rich, said the research used leading questions, creating the impression that a lot of advertising was directed at children, when this was not the case.
Food companies already adhered to strict rules, including those overseen by the Advertising Standards Authority. "They are stringent and clear codes and I'm not sure where they could be strengthened.
"The Children's Code for Advertising Food says food advertising should not undermine the wellbeing of children or government nutrition policy, and they shouldn't encourage over-consumption of any food, particularly treat food, snacks, or fast food."
Professor Swinburn urged a mix of new state regulations and beefed-up industry self-regulation, focusing first on controlling TV advertising and weaning children's sports off sponsorship from unhealthy food producers.
NZ Football commercial director Steve Brebner said commercial sponsorship of sport is a critical part of the organisation's funding model.
"Our commercial partnerships provide the resources to improve grassroots football in New Zealand and at an elite level. The feedback we receive from the parents of the nearly 50,000 Kiwi kids who play football each year is overwhelmingly positive about our programmes and sponsors," he said.
"With regards to McDonald's sponsorship of junior football, the funding is put directly into programmes that encourage and reward activity and participation at a local community level. Without the funding of long-term sponsors like McDonald's junior football would lack the tangible resources required to encourage involvement in New Zealand's most popular junior sport."
A spokesman for McDonald's said it was proud of its long-term sponsorship of kids' football which went into encouraging activity and participation, and reward development.
Mother cites television adverts' pester power
Auckland mother of three Dong Suk Kwak has strong opinions about children being exposed to junk-food advertising on television.
"Of course it's wrong.
"Strong restrictions should be on television for the junk food for children because it is unhealthy and more advertising means it is more attractive for kids."
She and her husband, Andy, do not permit their children - Joshua, 6, Suna, 4, and Sunauyu, 2 - to watch much TV, but even from the small amount they do see, Mrs Kwak is acutely aware of the pester-power effects on their junk-food demands.
"When they watch more they want to buy more, they beg me to buy more. It's hard to stop them.
"When they grow a little older they can choose by themselves what is good and what is not.
"When they are young, they don't know which one is really good, they cannot control themselves, so I think all the parents should have a guideline."
Claire Deeks, a mother, lawyer and promoter of unprocessed "real" food, said: "I would be in favour of some sort of oversight and reduction in advertising to children."
Her 4-year-old son Dominic - who eats chicken broth for breakfast - did not watch free-to-air television, except occasionally at day-care, "but naturally he is still exposed to advertising because it's everywhere".
"It's often the older children that are even more affected.
"Under 5, there is a good chance you can dictate a lot of what your child does when they are that age," Ms Deeks said.