A loophole exempting thousands of England's schools from healthy eating standards must be closed to combat child obesity, say council leaders.
New standards for school food became mandatory in council maintained schools and some academies in January 2015.
But for schools that became academies between 2010 and 2014, the food standards are voluntary.
Schools teaching about a million pupils have failed to adopt the code, says the Local Government Association, (LGA).
The standards restrict the amount of sugary, fried and fatty foods in school meals and require pupils to be offered at least one portion of vegetables or salad as part of their lunch each day
They are mandatory in all council schools, new academies and schools that became academies between 2008 and 2010.
But having to follow them was optional for the 3,896 academies and free schools that opened between 2010 and 2014, as their funding contracts allow them greater autonomy.
Rather than change their contracts, the government wrote to these academies to make a voluntary agreement to comply with the new food standards.
But, according to the LGA, 2,476 schools have still not formally committed to the standards.
The LGA argues it is essential the government uses a new childhood obesity strategy, expected this summer, to close the loophole and oblige all academies to commit to the same food standards as other state schools.
The LGA highlights official figures showing 3.5 million children are obese, putting them at a higher risk of diabetes, heart disease and cancer.
Izzi Seccombe, the LGA's spokeswoman for community wellbeing, called the lack of commitment to healthy meals from some academies "deeply worrying".
"It's not right that we have rules for some but not all," she said.
"The forthcoming childhood obesity strategy is a great opportunity for the government to close this loophole in legislation, which will make all academies follow standards that demonstrate a nutritional safety net to parents, who can be assured that their children are eating healthy food at school, rather than meals that could be laden in high amounts of fat, salt or sugar."
A Department for Education spokeswoman did not directly respond to the LGA's call for the loophole to be closed but said: "The new school food standards are ensuring more pupils eat good food that encourages healthy eating for life.
"They also make it easier for school cooks to devise nutritious, tasty and varied menus.
"Parents rightly expect every school to serve children a healthy lunch.
"All new academies are expected to meet the food standards, and we are pleased that more and more academies are signing up voluntarily."
