The Government's flagship free schools are opening up in disadvantaged neighbourhoods, but are educating fewer poor children on average, according to new research.
It also suggests that many of the primary-age youngsters attending free schools have higher levels of previous achievement.
Free schools are semi-independent state schools set up by teachers, parents and other groups that have a freedom over areas such as the curriculum and staff pay.
A key plank of the Conservatives' education policy, around 331 free schools are now open or approved to open.
The new study, by the Centre for Learning and Life Chances (LLAKES) at the Institute of Education (IoE) examined the intakes of of 88 primary and 63 secondary free schools which had opened by September last year.
On average, free schools are being set up in disadvantaged areas, the study found, but fewer pupils attending these schools are eligible for free school meals (FSM) - a key measure of poverty.
Around 13.5% of pupils attending primary free schools were eligible for FSM, it says, whilst within the neighbourhoods of free schools, 18.3% of youngsters were eligible for the dinners. Across the rest of England 15.9% of primary-age children were entitled to FSM.
The findings also show that 17.5% of pupils attending secondary free schools were entitled to free lunches, with 22.1% of youngsters eligible in the neighbourhoods and 17.3% eligible across the rest of England.
"The net effect is that the free secondary school pupils themselves are close to average for all secondary schools, and the free primary school pupils very slightly better off," the study says.
It goes on to show that there is a "marked difference" at primary school level in pupils previous achievement.
Free school children have a distinctly higher average Foundation Stage Profile score - from early years education - than elsewhere in the neighbourhood and the rest of England, the study suggests.
Study author Professor Francis Green said: "It appears that, so far, the places in reception at free primary schools are being filled by children who are somewhat less disadvantaged and more advanced in their development than the average. This outcome may be disappointing for the Government, which had hopes that its free schools policy would be a vehicle for delivering social justice."
Shadow education secretary Tristram Hunt said: "David Cameron is damaging our education system with his free school programme, taking standards backwards. By allowing unqualified teachers into the classroom and presiding over a widening of the attainment gap between the poorest children and the rest, we are seeing school standards suffer under this Tory-led Government.
"Labour will put an end to this damaging policy by introducing new local directors of school standards to raise standards for all children in all schools."
Natalie Evans, director of the New Schools Network said: "The fact is that free schools are being set up in the communities that most need high-performing new schools - they are 10 times more likely to be in the most deprived parts of the country than the most affluent.
"Free school founders are choosing to set up in more deprived areas precisely because they want to make the biggest difference to children that do have access to the high quality education they deserve.
"And as they become an established part of the education system it is becoming increasingly clear that free schools are proving popular with parents from all backgrounds."
A Department for Education spokesman said: "Delivering the best schools and skills for young people is all part of this Government's long-term economic plan.
"To help with this we have established more than 4,000 new schools that are responding to what parents and pupils want, and we have committed to helping pupils from disadvantaged backgrounds through new policies such as the pupil premium, which is worth £2.5 billion this year alone.
"Free schools are a vital part of this mix. They are offering parents more choice than ever before and allowing thousands more children the opportunity to go to an outstanding state school.
"Two-thirds are in the some of the most deprived areas of the country, and under this Government the attainment gap between pupils receiving free school meals and their peers is closing."