
The LGA states in its submission to the government ahead of the Spending Review in November, that there is a "serious lack of capacity and capability" within RSCs which "could risk children's education".
Under proposals in the Education for All Bill, councils' legal role in overseeing and improving school standards will come to an end, with ministers handing the responsibility to RSCs.
The LGA says it is unrealistic to expect commissioners to turn around all struggling schools. There are currently eight commissioners responsible for almost a quarter of schools in England, with each one working with, on average, nearly 100 academies that are rated less than good.
Instead, the association has called for councils to be given more powers to ensure schools are delivering high quality and value for money, as well as more say on where new schools are established.
It points to evidence that almost one in six academies and free schools have been rated less than "good" by Ofsted.
It states that 89 per cent of maintained schools are rated "good" or "outstanding", compared with 62 per cent of sponsored academies, 88 per cent of converter academies and 82 per cent of free schools.
Richard Watts, chair of the LGA's Children and Young People Board, said: "It is simply asking too much to expect RSCs to effectively turn around dozens of schools across a huge area.
"Placing more power in the hands of few unelected civil servants, who parents cannot hold to account at the ballot box is out of sync with the government's aims to devolve more decision-making and responsibility down to local areas and communities.
"With the government planning to end councils' role in supporting school improvement and intervening in failing schools from next year, we have yet to be convinced that RSCs have the track record or the capacity to take on responsibility for another 13,000 schools."
In its Spending Review submission, the LGA also calls on the government to scrap plans to cut £600m from the educational services grant, announced in last year's Autumn Statement.
A Department for Education spokesperson described the claims as "nonsense".
"It is inevitable that councils oversee a higher proportion of good or outstanding schools as failing schools are taken out of council control and converted to academies, where after being paired with a strong sponsor they stand the best chance of breaking from their often long histories of underperformance.
"All academies operate under a strict accountability system - more robust than in council-run schools. Regional school commissioners are an important part of that system and thanks to their oversight where issues are identified we will not hesitate to take swift action, something that the council-run system would fail to tackle for years."
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