Parents should have access to a single, local body responsible for holding their children's school to account, council leaders have said.
The Local Government Association (LGA) said it is calling for the next government to make all state schools work together in education "trusts".
These trusts, which could be set up in every area of England - and overseen by councils, would be a single point of contact for families and cover all types of state school, including academies, free schools and those run by local authorities, it said.
The LGA said while councils are still responsible for 84% of schools, they currently lack adequate powers to hold these schools to account.
At the same time, there are 3,500 academies and free schools that are not under local authority control and are accountable to Whitehall, the association said, which it argued does not have the capacity and local knowledge to oversee them.
Proposals for the new trusts form part of a new report published by the LGA.
Schools would be at the centre of the trusts, which would play a key role in school improvement and in helping every school to get an Ofsted rating of good or better, the association said.
Councillor David Simmonds, chairman of the LGA's children and young people board, said: "Every child deserves a good education at a local school and establishing education trusts will empower councils to ensure this happens across their local area.
"The current two-tier system of accountability is confusing for mums and dads to navigate and with different organisations responsible for different elements of education, there are too many possibilities for issues raised by mums and dads to slip through the net.
"Education trusts would strip away this bureaucracy and provide an easily identifiable place which parents can turn to. Someone has to take responsibility for the accountability of schools and with local knowledge and links to the community councils are ideally placed to take this role on their education trust."
A Department for Education spokesman said: "Academies take power away from politicians and bureaucrats and give it to the heads and teachers who know their pupils best. Results are rising faster in sponsored academies than in council-run schools, and converter academies are more likely to improve their Ofsted rating.
"We are strengthening the failure regime for academies through the new Regional Schools Commissioners and Head Teacher Boards. This will ensure swift action is taken in the small number of cases where academies are struggling.
"It is thanks to this Government's reforms that the number of pupils being taught in failing secondary schools has fallen by 250,000 since 2010."