All bright children should be given the chance to go to private school, an education expert said, as he warned that the UK's schools are socially divided.
Academic selection of pupils, widespread in the 1970s, has been replaced by social selection, according to Sir Peter Lampl, chairman of the Sutton Trust.
It is now more difficult for poorer children to improve their chances in life than in the past, he argued.
Speaking at the Headmasters' and Headmistresses' Conference (HMC) annual conference in Belfast, Sir Peter urged heads to back a scheme aimed at allowing more bright children from all backgrounds to gain places at private schools, based on merit rather than ability to pay. Social mobility - improving an individual's life chances - is "the biggest social issue of our time", Sir Peter said, and is "on the political map like never before".
A study conducted for the Sutton Trust by the London School of Economics (LSE) found that Britain, together with the US, has the lowest levels of mobility of any developed country for which there is data, he told the conference.
"Put simply, it is very difficult for children from less privileged backgrounds to move up in society and it is more difficult than it used to be. It's got worse," he added.
Sir Peter also cited an international study which found that inequality has increased faster in Britain over the last 30 years than any other developed country and is one of the highest in the world. "We got rid of academic selection in the 1970s and this has simply been replaced by social selection," Sir Peter said. "Our selective universities and many of our professions are effectively closed to a large number of young people."
Some 7% of English pupils go to private school and another 4% attend selective grammar schools. These grammar schools attract just 2% of youngsters on free school meals - a measure of poverty. The top comprehensive schools take just 6% of their pupils from the poorest homes, Sir Peter said.
He added: "I believe we should address this inequality in three ways. First, comprehensives should use ballots to determine admissions to urban secondary schools to ensure a social mix."
"Secondly, grammar schools should reach out to able students from poorer families. The third solution should be to transform the independent sector, ensuring that day schools recruit once again on merit rather than money, opening them up to a wider pool of talent."