A spokesman for the Children's Food Trust said evidence shows that schools are offering healthier meals and children are eating more nutritious lunches since national school food standards were put in place.
A Department for Education spokeswoman said if the Local Government Association has evidence of academies and free schools providing unhealthy meals to their pupils then it should be released.
Chairman of the Local Government Association's children and young people board, David Simmonds, said the current Government strategy on healthy school meals has resulted in a "two-tier system".
Mr Simmonds said:
More than a million children could be eating unhealthily at lunchtime because their schools are exempt from tough food standards, council leaders have warned.
Free schools and academies that opt out of national regulations are "ducking their moral duty" to make sure school children receive healthy meals, according to the Local Government Association (LGA).
The LGA issued a fresh call to the Government to introduce a single standard that applies to all schools to ensure every pupil has access to a healthy lunch.
Sir Merrick, leader of Kensington and Chelsea Council in London, asks the Government to commit to capping the amount people will have to pay for their elderly care and working to ensure it is successfully implemented.
Last year an official commission chaired by the economist Andrew Dilnot recommended that the state should pick up the cost of care beyond £35,000, at an estimated cost to the public purse of less than £2 billion. The LGA letter says the proposal is an expensive but worthy investment.
In his letter to the leaders of all three main political parties, Sir Merrick, leader of Kensington and Chelsea Council in London had suggestions for reforming care for the elderly:
The letter also calls for improved efficiency in reform, including pooled budgets to provide further benefits for individuals.