"A wide range of research places Britain at or near the bottom of the league table of mobility, particularly in terms of the link between children's educational achievement and parental income.
"The public appear to recognise some of the inequalities in our society, but on the face of it half do not think that Britain is particularly socially immobile."
The Department for Children, Schools and Families said progress had been made tackling poverty.
Education focus
A spokeswoman said: "As the prime minister said this week, the government's vision is to create a Britain where everyone, no matter what their background, can make the most of their potential.
"We know that deprivation and poverty in the long term can only be tackled by changing the aspirations of young people and their parents.
"We are accelerating this change by creating a world-class education system."
Gordon Brown said improving social mobility in the UK was a "national crusade" but conceded Labour had not yet made enough progress.
The prime minister also announced a £200 grant for deprived families in England who joined schemes to improve children's development.
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