Poor pupils and those who receive free school meals are "significantly" less likely to be admitted to grammar schools, a study branded "disturbing" has revealed.
Even pupils who achieve higher grades than their richer peers are still battling against the odds to attend an academically selective school, according to the Institute for Fiscal Studies report.
The study also shows grammar schools are four times more likely to admit private school children than those on free school meals.
The 'Entry into Grammar Schools in England' paper found "bright pupils from deprived families are not attending grammar schools as much as their attainment would suggest they might".
There are 164 grammar schools in England, which select pupils on the basis of performance in entry tests in Year 6. These schools educate 4% of the Year 7 pupils in England.
Tunde Banjoko, founder of LEAP, a charity improving the lives of disadvantaged young people, told The Huffington Post UK: "These findings are disturbing but depressingly unsurprising.
"A large swathe of our children are having their chances of fulfilling their academic potential affected through no fault of their own, but rather because they come from a poorer family. It is an example of the Matthew Effect and has long-lasting detrimental consequences, not only for the unfortunate children who are passed over, but for society as a whole.
The report uses maths attainment as an example of pupils who are eligible for free school meals (FSM) having a "noticeably" lower probability of attending a grammar school.
"A non-FSM student with an average maths score has the same probability of entering a grammar school as an FSM pupil with a score 0.7 standard deviations above average.
"Non-FSM pupils with test scores one standard deviation above average have a 55% likelihood of attending a grammar school in selective local authorities, whereas similar pupils who are eligible for FSM have only a 30% chance of attending a grammar school."
A spokesperson for the National Grammar Schools Association said: "The reason pupils are admitted to grammar schools is if they pass the 11+ test. It is nothing to do with their conditions of primary school education."
The chairman of the National Grammar Schools Association, Robert McCartney, said there was nothing "significant" in the conclusions of the report.
"Many, many parents from deprived areas, including what is generally called the dependency classes, are essentially not particularly interested in any form of academic education," he said. "Their interests are directed towards pop culture, sports."
But one headteacher Tom Sherrington added:
The report admits it is "unclear" whether poorer pupils are less likely to attend grammar schools because they come from poor families or because they possess "other characteristics" which affect their chances. Examples of such attributes include lower levels of attainment or living further away from a grammar school.
Anna Vignoles, professor of education at Cambridge University and one of the report's authors, told HuffPost UK a comparison could be drawn between grammar school selection and admittance into some higher education institutions; both are based on academic selection but disadvantaged students may not apply as they may believe they are not capable of success.
However, she added: "Given that [grammar schools] are part of the state system, it would be possible for the school system to do something about these students not applying.
"There should be an automatic application process or more encouragement for these pupils to apply."
The report adds: "Those living in an area in the most deprived 20% of neighbourhoods are 13.1 percentage points less likely to go to a grammar school than pupils in the top quintile.
"The estimated FSM gap is over 12 percentage points amongst pupils who achieve level 5 [the top level]."
Additionally, pupils' ethnicity plays an "important" role in whether they attend a grammar school; pupils from non-white ethnicities are more likely to attend than similar white pupils. This trend is particularly strong among Asian and Chinese students.
"Eligibility to FSM and being white are associated with lower probabilities of attending a grammar school," the paper continues. "It is possible there are cultural preferences towards education that could lead to higher attendance at grammar schools.
"If a greater weight is placed upon entering a selective school, these pupils may prepare more for entrance tests than white
children do. A greater preference for a selective education could lead to pupils from ethnic minority backgrounds being more willing to travel further to a grammar school than similar white children.
"It is also possible that high-ability minority ethnic children are more likely to be encouraged to apply for entry into a grammar school."
Although the study does not have the answer as to why FSM pupils are less likely to attend grammar schools - Vignoles explains they "can't" - the authors do attempt to offer some possible explanations.
"First, they may be more likely to apply, either because they have a preference to attend a high-performing school with other bright children or because they are more strongly encouraged to apply, by their parents and/or by their primary school.
"Second, conditional upon applying, high-achieving children are more likely to do well in the entrance tests, and therefore are more likely to gain admission to a grammar school. As such, the effect of KS2 attainment may be a combination of a greater chance of applying and, having done so, a greater chance of passing the entrance exam. "
In certain local authorities, pupils eligible for FSM are "much less likely" to attend grammar schools. According to the study, a "good proportion" of this gap can be explained by the fact poorer pupils display lower levels of academic achievement by age 11, and are therefore presumably less likely to pass entrance exams.
"However, amongst those pupils with high levels of academic attainment, poorer pupils are still much less likely to attend grammar schools," the report adds.