Many primary schools in England take in pupils whose family circumstances are very different from the neighbourhoods they serve, research suggests.
The study questions how much schools reflect their communities
Primary schools are not meant to select which pupils they admit.
But a study by think tank Iris found Catholic schools in particular had almost 9% fewer children from low-income groups than was expected.
Pupils in church schools also tended to have better results in their national curriculum tests.
Iris - the Institute for Research in Integrated Strategies - commissioned a study of 391 primary schools: 287 community schools, 56 Church of England, 47 Roman Catholic and one Jewish.
They were in three randomly-chosen urban local authorities, in London and in the north and west of England.
Using 2003 data, it compared the proportion of pupils at each school who were poor enough to qualify for free school meals with the proportion of such children in each school's postcode district.
If all pupils attended their nearest school these figures would be expected to be similar, its report said. But the study found big variations.
One school with only 10% of pupils on free meals was in a postcode with over 45%.
Overall, non-religious community schools tended to have slightly more poorer pupils than expected.
Church schools had fewer. Catholic schools, in particular, had almost 9% fewer poor pupils than in their neighbourhoods.
The report's author, Chris Waterman, said it was difficult to be categorical about the reasons for the apparent variations.
Possible reasons included:
But Mr Waterman said there was at least a case for doing further research on a nationally representative sample of schools.
- church schools draw from a relatively wide geographical area
- schools with a good reputation but more spaces than local children need might also take pupils from a wider area
- middle class parents might be more motivated to seek a school that is not their local one
- the areas chosen for the study might not be typical
- a school may not sit in the 'middle' of the postcode sector
- in some sectors there could be more than one primary school
- some pupils might cross the local authority boundary to attend school
A spokesman for the Catholic Education Service said the most likely reason was indeed that Catholic schools served a much wider geographical area than their immediate postcode.
"Indeed, the research shows that some Catholic schools have a much more socially disadvantaged intake than their location would suggest," he said.
"The Catholic Education Service is clear that Catholic schools should not be socially selective.
"We have consistently argued that schools should not interview potential pupils or their parents.
"Instead, governing bodies should ensure that the admission process to Catholic schools is always as transparent, straightforward and undaunting for applicants and their families as possible, whatever their background."
The Iris report also suggested that far from being free at the point of delivery, many schools were "quite expensive" as a result of "covert selection".
For example, they might require a distinctive blazer - from an upmarket supplier - rather than a stock coloured sweatshirt.
Others made much of the voluntary contribution parents were expected to make to school funds, which required "a certain determination in a parent unable to pay".