Evidence that academy chains can improve pupils' results is "limited and varied", MPs have warned.
The Commons Education Select Committee has raised concerns about the performance and expansion of "multi-academy trusts" (MATs), arguing that while some are producing good results, others are failing to improve and are languishing at the bottom of league tables.
These organisations are responsible for running groups of academies - schools that are free from local council control and have freedom over areas such as the curriculum and staff pay.
In a new report, the cross-party group of MPs says that some of these trusts have expanded too quickly and the performance of their schools has suffered, while more must be done to ensure that they can be properly held to account by Ofsted and local communities.
The number of schools joining MATs has grown significantly over the past five years and the Government predicts that in the next five this will grow further, the report says. It is now expected that most schools which take on academy status will join a MAT.
There are 1,121 MATs in England, as of 2016, it says, up from 391 in 2011. As of March last year, 65% of academies and free schools were part of a trust.
"However, evidence of their ability to raise pupil performance is limited and varied," the committee says.
"The picture across England is very mixed with academies in trusts at both the top and bottom of recent league tables.
"Some of the earliest trusts expanded too quickly over wide geographic regions and the performance of their schools suffered as a result."
The committee says it is encouraging that a MAT "growth check" is being developed and urges the government to use this to ensure that trusts are only allowed to take on more schools when they are ready.
The report adds that there are gaps in how trusts are inspected and Ofsted should be given powers to conduct full inspections of them and they must engage more with parents.
It also notes that more academy sponsors are needed as certain areas are struggling to attract new ones.
Committee chair Neil Carmichael said: "Since launching this inquiry there have been several changes to academy policy which have caused uncertainty and instability in the sector.
"We have significant concerns about the performance, accountability and expansion of multi-academy trusts.
"While some MATs are producing excellent results and making a valuable contribution to our education system, a considerable number are failing to improve and are consistently at the bottom of league tables.
"MATs have emerged from the Government's plan to increase the number of academies but policy and oversight have been playing catch-up.
"Only time will tell if MATs are more successful than local authorities in tackling under-performance and supporting high-performing schools.
"But if the Government is to pursue the goal of further academisation, it will need to work with local authorities and allow those councils with a track record of strong educational performance to use their expertise within their education department to create MATs."
Richard Watts, chairman of the Local Government Association's Children and Young People Board, said: "The LGA has long been concerned about the lack of local accountability, financial oversight and governance arrangements that exist for multi-academy trusts.
"With 91% of maintained schools now rated as either outstanding or good by Ofsted, now is the time for government to recognise councils as its education improvement partners.
"Schools should be given the freedom to choose, in partnership with parents and councils, whichever structure is most appropriate for local children and if that means councils setting up their own MATs then they should be able to do so."
A Department for Education spokesman said: "Thanks to our reforms there are now almost 1.8 million more children being taught in schools rated good or outstanding schools than in 2010.
"The best multi-academy trusts are turning round struggling schools across the country and providing good school places for thousands of children.
"The oversight and accountability system for academies and MATs is more robust than LA maintained schools, allowing us to take swift action to deal with underperformance.
"Where an academy is failing to reach the standards we expect, action is taken including transferring schools to new trusts.
"We are already developing a 'growth check' to ensure good trusts only take on new schools when they are ready and it will not impact on the education of the children they are already responsible for.
"Local authorities are already able to be part of a MAT with up to a fifth of its board having links to their local authority.
"We encourage all trusts to work collaboratively and the best already do so but maintaining their independence is a crucial part of encouraging the innovation that has driven up standards in so many schools."