The top universities in England have been told to start increase places for disadvantaged students.
The university watchdog, the Office for Students, wants the “access gap” between wealthier and poorer students to be halved in five years.
Young people from affluent areas are six times more likely to get places at the most selective universities.
“It is damning for the sector that large gaps still remain,” said Universities Minister Chris Skidmore.
“We cannot let this talent be wasted.”
But private schools’ leaders said universities should not “discriminate” against their pupils.
The Office for Students said despite an increase in the overall number of students, the proportion of disadvantaged students in most selective universities had “hardly changed”.
Oxford recruits 15 students from the most advantaged areas for every one student from the least advantaged – with a target of reducing the ratio to eight to one.
Mike Buchanan, executive director of the Headmasters’ and Headmistresses’ Conference group of independent schools, said young people should not be discriminated against because of the “class they were born into”.
He said universities should be expanded to “take as many truly suitable students as necessary, rather than rob some students of a future to award it to others”.
Mr Buchanan also called on universities not to increase international student numbers if it denied places to UK students.
