Many academy chains are letting down poor, bright pupils, according to research.
A new study suggests that disadvantaged youngsters who were performing well at primary school make less progress in sponsored academies than in other types of state school.
The research analysed the performance of poorer pupils - those eligible for the pupil premium - attending secondary schools run by academy chains between 2014 and 2016.
The study, published by the Sutton Trust, analysed 48 chains - organisations that run groups of schools.
It found that on average, disadvantaged pupils at secondary schools in an academy chain who were lagging behind at the end of primary school made more progress by the time they took their GCSEs than those in other types of school.
Overall, there were 26 out of 48 chains where poorer pupils with lower grades at the end of primary school made more progress than in state schools in general.
But the study also shows that clever poor youngsters who were in the top 20% at the end of primary school, performing above the level expected for the age group, made less progress in these academies than those in other types of state secondary.
Sutton Trust chairman Sir Peter Lampl said: "As our research shows, more than half of academy chains are doing a great job for their disadvantaged pupils.
"However, the problem is there are only eight chains out of 48 where poorer pupils who are in the top 20% at the end of primary school make more progress than those in state schools.
"So many high-attaining pupils are failing to fulfil their early academic potential in these schools.
"The Sutton Trust has long been advocating that high-attaining students in academies should have the support and guidance they need to thrive.
"The Government should create a fund to enable these students to succeed."
Study author Professor Becky Francis, director of the UCL-Institute of Education, said: "It is heartening to find that a majority of academy chains are effectively supporting their pupils with low prior attainment; something that schools in England have often struggled to achieve.
"However, they need to extend this to ensure they are supporting the progress of all their disadvantaged pupils.
"As well as the importance of this for life chances and social mobility, this will be necessary to drive up attainment in sponsored academy chains, which is still problematic for many."
A Department for Education spokeswoman said: "The attainment gap between disadvantaged children and their peers is narrowing but we know there is more to do, which is why we are taking a range of actions including investing £2.5 billion through the pupil premium to support disadvantaged pupils and our Opportunity Areas programme to raise standards in 12 areas across the country."