Church primary schools in England are less likely than local authority schools to admit children from poorer homes, updated research shows.
The report suggest parents shop around for primary schools
In 2005, the Institute for Research in Integrated Strategies identified a similar phenomenon in a limited study.
It has now analysed admissions and eligibility for free school meals in all 17,319 primary schools in England.
Schools in the voluntary aided category admitted fewer poorer children than expected from the area's social makeup.
Almost 19% of children living in the postcode area of church schools were from families eligible for free meals, but only 14% of the schools' intakes were.
Conversely, local authority community schools took a slightly higher proportion of poorer pupils than lived in their local districts.
The institute's report suggests league tables are encouraging parents to "shop around" for primary schools as much as for secondary schools.
The author, Chris Waterman, suggests that other factors, such as the costs of school uniform or extra-curricular activities, could be producing a form of social sorting - determining which parents apply to certain schools in the first place.
His original study of schools in three areas, published in November, suggested Catholic schools in particular did not reflect their local areas - taking fewer poor children.
At the time, the Catholic Education Service said the most likely reason was that its schools served much wider geographical areas than their immediate postcodes.
The Church of England's chief education officer, Canon John Hall, said the figures in the new report were complicated and did not give enough information about the localities and densities of neighbouring schools.
"As the author acknowledges it is hard to generalise about primary school admissions - though he seeks to do so," he said.
He added: "If there were covert social selection for church schools - of which there is no actual evidence in this report - we would deplore it and seek to root it out.
He was in favour of a proposal by the Commons education select committee to strengthen the powers of the local forums which seek to co-ordinate admissions in each area.
"We would welcome the monitoring of admissions practice by the local admissions forum and the strengthening of diocesan powers requiring governing bodies of voluntary aided schools to follow the advice they have been given," he said.