Business Secretary Vince Cable said going to university should be about "ability, not ability to pay".
It comes as a report has found that top universities are not doing enough to recruit students from poorer families.
A Cambridge University spokesman said: "Since this reporting period, which relates to 2010 entry, the University has made significant steps towards our key milestone of increasing state sector admissions without compromising academic standards.
"In September 2012, 63.3% of our UK first years came from the state sector, the largest proportion for thirty years. This exceeds our original objective and reflects attainment in UK schools."
An Oxford University spokesman said: "We have worked incredibly hard to ensure that any student with the academic ability to study at Oxford can do so regardless of financial circumstances.
"By spending more of our additional fee income on outreach and bursaries than any other mainstream university, we are able to offer the best no-strings financial support package for the poorest students in the country."
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