Oxford and Cambridge were criticised by a Government minister for failing to give enough places to working class students.
Higher education minister Bill Rammell said the two ancient institutions take only one in 10 of their students from working class backgrounds.
There is "no excuse" for any university to "wash its hands" of the need to help more students from poor homes get degrees, he said.
Overall, only 20% of pupils from lower income groups finish school and go on to university.
One in five students in the Russell Group of leading research universities come from lower social groups, Mr Rammell said.
"And at Oxford and Cambridge, it's one in 10," he said.
"I know the causes for that inequality of opportunity are complex and not confined to universities' admissions policies.
"There's work that must be done in schools as well and, as a Government, we're doing it.
"But that's no excuse for any university to wash its hands of the problem."
Mr Rammell's remarks represented a rare decision by the Government to criticise Oxford and Cambridge by name.
Ministers have repeatedly called for "sought after" universities to make sure they are doing all they can to open their doors to working class students.
But in recent years they have usually stopped short of identifying individual institutions.
Mr Rammell said the Government's policies were making university campuses "more representative" of society.
"But the talent of all our people deserves to be unlocked and we all have a part to play in ensuring that it is," he said.
"Over our history, we've let too much of it go to waste by lying undeveloped.
"In an increasingly knowledge-driven world, we can't afford to let that happen.
"Now is the time to quicken the pace of change."
In 2000, Laura Spence, a high-flying state-educated student from Gateshead, provoked a major row after she was refused a place at Magdalen College, Oxford.
Gordon Brown, the Chancellor at the time, described her situation as "an absolute scandal".
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