Research for Sutton Trust charity says some schools are taking a higher proportion of wealthier children compared to the numbers in the neighbourhood.
The Sutton Trust said that these schools, many of which are Christian, are using admissions rules which risk leaving poorer children at risk of losing out.
It has also criticised faith schools that used religious criteria to award places if the school is over-subscribed.
Their research calculated the proportion of children on free school meals (FSM) at a school, a key measure of poverty, and compared it to the proportion children on free school meals in the school's catchment area.
It stated: "In these schools, over-subscription criteria are often faith-based, with governing bodies taking the final decision on admissions.
"This gives greater choice of schools to church-going families, but this also exacerbates inequalities in choice because those families are more likely to be of a higher social class.
"Such criteria and decision-making systems contribute to the divergence in FSM intake of the most socially selective schools."
Paul Barber, Director of the Catholic Education Service, commented: "Catholic schools are the most ethnically and socially diverse in the country, educating more children from the most disadvantaged backgrounds than the national average.
"This report fails to take into account that catchment areas for Catholic schools are ten times the size of other schools, significantly increasing the number of potential applicants.
"What's more, because of the high standards achieved by Catholic schools they are extremely popular with parents of all faiths and none.
"We do however, welcome the report's recommendations that religious admissions criteria should be simple, consistent and properly enforced, and we work closely with the Office of the Schools Adjudicator and the Government to achieve this."
A CofE spokesperson said: "Church of England schools are there for the whole community and serve children of all backgrounds.
"We have not had the opportunity to review the Sutton Trust's research as yet but will look at it with interest."