Parents are "frustrated" that their local councils cannot intervene where there are concerns about schools' performance, according to the Local Government Association (LGA).
Cllr David Simmonds, chairman of the LGA's Children and Young People Board, said: "Parents deserve a local organisation to act as a first port of call if they are not satisfied with the response from their child's school or its governing body.
"Mums and dads concerned about their children's education will always turn to their local council for help. But they are rightly becoming increasingly frustrated when their council is unable to intervene."
More top news
After the Indiana polls close, ITV News asked Ted Cruz supporters if they could back Donald Trump as the Republican presidential nominee.
With his massive victory in Indiana, Donald Trump can now not be stopped from becoming the Republican nominee.
Donald Trump is predicted to win the crucial Republican Indiana primary, US media have projected.