Claims by council leaders that more than a million children at academies and free schools could be eating unhealthy meals are rejected by these schools and the government.
Academies and free schools are exempt from the national food standards maintained schools have to adhere to, and the Local Government Association (LGA) says it fears that schools that opt out of these standards are failing in their moral duty to ensure pupils eat healthily.
It wants the government to introduce a single standard that applies to all schools, including academies and free schools, which are outside local authority control.
David Simmonds, chairman of the LGA's children and young people board, said: "School autonomy is supposed to drive up standards, but in the case of school meals we now have a two-tier system where one type of school can effectively exempt pupils from healthy choices and instead sell fatty and sugary foods.
"This threatens to seriously impact on the health and educational attainment of our children."
Nick Weller, vice chairman of the Independent Academies Association, which represents academy schools, told Channel 4 News that these schools took nutrition extremely seriously.
The Jamie Oliver effect
Mr Weller, who is executive principal of Dixon's Academies in Bradford and eats school lunches with his pupils, said the celebrity chef's influence had had a marked effect on nutrition in academies.
"I would say that it's almost written into the DNA of academies because the movements were contemporaneous.
"I know of a number of academies that take the food that their children eat very seriously. It's often one of the first things that academy chains will look at very early on when they move into a school.
"Academies tend to work a longer working day and therefore they're not just feeding children at lunchtime. Getting nutrition throughout the day is key to concentration and learning."
Under the current system, academies and free schools do not have to comply with the same nutritional standards, introduced by the last government, that apply to other state schools.
Jamie Oliver has also raised concerns about food in academies, which now make up more than half of all secondary schools.
But the Department for Education said: "If the LGA has hard evidence of academies providing poor food they should release it.
"The School Food Trust's research shows that academies do no worse than council-run schools on food standards and outperform them in many.
"Far from being the best example of nutrition, many council-run schools are not meeting food standards and are offering cakes, biscuits and fizzy drinks to their pupils. Others have said they find the standards too bureaucratic, rigid, and difficult to administer."
Academies were first set up under Tony Blair's Labour government, with the aim of raising standards in under-performing schools in disadvantaged areas.
The coalition Government opened up the programme in 2010 to allow good and outstanding state schools to convert to academy status.
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