The school admissions code should be radically overhauled to give more children from poor homes places at top-performing state schools, according to the head of a leading grammar school.
Shaun Fenton, chair of the newly formed Grammar School Heads' Association (GSHA), said pupils from disadvantaged backgrounds should be given priority over children from middle-class homes in a bid to improve social mobility.
Poorer pupils could be treated in the same way as children in care, who are given precedence when popular schools are oversubscribed, suggested Mr Fenton, head of Pate's Grammar School in Cheltenham.
Appeals panels which listen to complaints from pupils who have failed to win places at their chosen schools could also take social background into account in reaching their decisions, he said.
The association, which was officially launched last week, has commissioned research into whether 11-plus tests need to be changed so they do not favour children from more affluent homes. Redesigned tests that do not favour children from middle-class homes could be implemented.
New versions could be designed to test pupils' longer-term academic potential, rather than their ability to recall certain facts. This would cut the benefits of private coaching that some critics believe give an added advantage to middle-class pupils under the current system.
"Grammar schools exist to serve social mobility, but they are not allowed to make allowances for the social background of applicants," Mr Fenton said.
"At the moment, the admissions code is written to be blind to background because of the danger that schools would take advantage of it."
Mr Fenton said the difficulties of serving a more socially diverse range of pupils were common to comprehensives in affluent areas as well as grammar schools.
The Sutton Trust education charity commissioned research last year which showed that the majority of the most socially selective state schools are not grammars.
But the study also found that grammar schools enrol only half as many academically able children from disadvantaged backgrounds as they might.
The research, which only looked at the top 25 per cent of academic achievers at 11, found that just under 2 per cent of those children in grammar schools receive free school meals, compared with 5.5 per cent in non-selective schools.
"This is not just a problem for grammar schools," Mr Fenton said.
"All schools should make the admissions code aid social mobility. It is about social justice, not social engineering."
Before its official launch, the new association has already been working with the Sutton Trust and holding meetings with the Department for Children, Schools and Families.
Mr Fenton, who was previously a comprehensive school head at Sir John Lawes School in Harpenden, Hertfordshire, said the remaining 164 grammar schools have an important role in ensuring that the system meets the needs of the brightest children.
"A lot of policy is rightly focused at intervening when things are not going well," he said. "But there is room for a voice saying how we can make sure things work for students aiming for high grades. Their need can be a forgotten need."
David Davis, the Tory MP and former shadow home secretary, last week called for a return to grammar schools to "rescue the next generation of the underprivileged".
But the Tory leadership has maintained a consistent position since David Cameron became leader that it will not support a widespread return to selection.
Mr Fenton said the launch of the association was not timed with an eye on a general election within the next year. He said it would not be campaigning to save schools, such as St Bernard's Catholic Grammar in Slough, Berkshire, that are slated for closure.
"We support grammar schools as part of a diverse provision of education," Mr Fenton said. "But if it works locally for a grammar school to become an academy, that is a decision to be made locally. Gradual evolution is fine."
There are 164 grammar schools dotted around England, but with concentrations in counties such as Kent, Buckinghamshire and Gloucestershire
They educate 4.9 per cent of the secondary school population: 158,610 pupils - up from 157,410 in 2008 and 156,800 in 2007.