More support for poor children is needed if Britain wants to overcome the educational attainment gap between rich and poor, researchers have said.
The report compared eight countries in Europe and North America
A London School of Economics report said Britain had relatively low "social mobility", as measured by earnings.
More poor children now stayed at school beyond 16 but university expansion had benefited the better off, it confirmed.
Philanthropist Sir Peter Lampl, who commissioned the study, said school "choice" applied only to the affluent.
"Those from less privileged backgrounds are more likely to continue facing disadvantage into adulthood, and the affluent continue to benefit disproportionately from educational opportunities," he said.
All the main political parties say they would improve the education system to give children better access to good schools.
But Sir Peter Lampl said parental "choice" would still be a reality only for affluent families with cars.
"Who is exercising choice?" he said. "It's pretty obvious. There is a lot of rhetoric by the politicians about school choice but making it practically available to everybody just isn't happening."
The report is mainly historical and defines mobility in terms of the adult earnings of children born to families at different ends of the income scale.
Researchers combined their own analysis of Britain, the US, [West] Germany and Canada, with other work on Britain, the US, Sweden, Norway, Finland and Denmark.
Role of education
The British focus was on boys born in 1958 and in 1970.
Many more from the poorest quarter remained in the poorest quarter as adults in the more recent study, the report said - while among the most affluent, far more remained affluent.
The researchers assessed the role of education, noting that "many commentators and political parties link mobility and the education system", and also included more recent children.
"Over the 1990s young people from poorer backgrounds have clearly taken up the opportunity to stay on in post-compulsory education, as never before," they said.
But the report confirms previous studies such as that by the Higher Education Funding Council for England showing that at degree level, inequality rose.
"The clear conclusion here is that the expansion of higher education in the UK has benefited those from richer backgrounds far more than poorer young people."
They found a "causal" link between family income and educational attainment but this was "modest".
So reducing child poverty would help, but only to an extent.
"We need also to use more direct means such as early years' education, improved schools for poor communities and financial support to pursue post-compulsory education."
This was the policy direction the government seemed to be taking, they said.
But this was currently "insufficient for the task at hand".
The report makes no mention of the abolition of most grammar schools - accessible on academic merit rather than affluence - during the years under review.
But one of the researchers, Professor Stephen Machin, told The Times: "The grammar school system was seen at the time as being very elitist. But it is ironic that probably that system got more people through from the bottom end than the system we have today."
The Labour Party proposes making it easier for successful schools to expand - but specifically excludes grammars from that policy.
The Conservative Party says it would let good schools expand, creating extra places so that within five years 100,000 more people would get their first choice of school.
The Liberal Democrats say choice will not exist until there is a consistently high standard of education for all children, with high quality teaching appropriate to their age, needs and interests.
Report: Intergenerational Mobility in Europe and North America by Jo Blanden, Paul Gregg and Steve Machin at the Centre for Economic Performance, London School of Economics.