England's universities should give pupils from poor backgrounds guaranteed interviews and lower offers, a key report on social mobility says.
Alan Milburn wants universities to "redouble their efforts" to give places to all those with talent and potential.
He says universities spend too much on bursaries and tuition fee waivers.
Money should be targeted at schools instead, adds the former Labour MP, asked by the government to review policies around social mobility.
Mr Milburn acknowledges recent progress on getting more pupils from non-traditional backgrounds into university.
But he warns: "Universities will need a new level of dogged determination if progress is to be made."
He calls for statistical targets on widening participation and a commitment to ensure that all outreach programmes have "maximum social impact".
And he says: "Universities should offer guaranteed interviews and, where appropriate, lower offers to less-advantaged pupils in schools they support."
He also wants them to provide bright poor pupils with the chance to study for a foundation degree if they have lower grades than they would usually ask for.
The report is likely to fuel the debate surrounding "social engineering" in university admissions and lead to fresh fears privately educated children will face discrimination.
Mr Milburn claims poor GCSE and A-level results remain the biggest barrier to higher education and says universities' efforts should be channelled towards intervention at a much earlier age.
Some of the money they currently spend on fee waivers and bursaries would be better targeted at getting 16-year-olds to stay on in education, achieve good A-levels and get into higher education.
This follows the scrapping of the education maintenance allowance in England last year after ministers claimed most of the money was "dead weight" - going to students who would have attended sixth form or college anyway.
Mr Milburn told the BBC: "The best thing that can be done in my view is to try to get kids to stay on at school after 16, to study hard, work well, get their A-level results and then progress on to university.
"So one of the things that universities can look at doing, following the government's decision, which I think is regrettable, to abolish the education maintenance allowance, is to provide a financial incentive for poorer families to get their youngsters to stay on at 16 rather than going into work because that way they stand the best chance of getting into higher education."
Mr Milburn's report, which is published on Thursday, also calls for a foundation year programme in all universities, where less advantaged youngsters will have the opportunity to catch up with their peers.
He also wants the most selective of universities to sponsor a city academy school.
Universities minister David Willetts welcomed the report and said institutions should seek to broaden access because making sure talent is spotted, not wasted, would ensure this country "has the skills to grow".
He said his own reforms were delivering significantly more investment in outreach, retention and financial support for disadvantaged students.
"We will consider his recommendations carefully and urge universities to do so too," he said.
Prior to the report's publication, Mike Nicholson, director of undergraduate admissions and outreach at Oxford University, said his university was already working hard to attract a wider range of student and made tutors aware of students' backgrounds.
Oxford now had 17,000 applications for 3,200 places, compared with 13,000 just five years ago, he said.
Certain groups in society that might previously have expected places at the university would now find competition fiercer, he said, adding that students who may have been admitted 10 to 20 years ago probably would not be admitted now.
"But that's not necessarily a bad thing at all - what we're doing is reaching out to a much broader range of students and making it possible for them to see themselves at Oxford," he added.
Professor Eric Thomas president of Universities UK said: "The report recognises rightly that school results remains one of the biggest barriers preventing students from disadvantaged backgrounds progressing onto university.
"While some universities do consider lowering their requirements by one or two grades, this is part of a much wider process in which the university considers a range of factors alongside an applicant's grades," he added.
Dr Wendy Piatt, director general of the Russell Group, said: "Grades at GCSE, A-Level or their equivalent are always hugely important, but they're never the sole criterion.
"There are lots of other things we take into account, for example some universities interview candidates precisely because they want to make sure that any strengths that are not reflected in their A-level results are actually brought out."
President of the National Union of Students Liam Burns said Mr Milburn was right to say the government should immediately cease funding "fictional, partial fee waivers", but added that reducing upfront financial support would also have questionable merit.
"Our own evidence suggests that those students from the poorest backgrounds are most likely to cite financial hardship as the biggest reason for dropping out, which shows the importance of continued funding for bursaries," he added.