The UK's top universities, among them Cambridge, should be halving gaps in the numbers of disadvantaged and advantaged young people taking up degree places in the next five years, a watchdog has said.
The most selective institutions have agreed on tough targets with the Office for Students (OfS) for the next five years as part of attempts to improve access for all would-be students.
Access to university has been a "postcode lottery" in the past, with young people from some parts of England much less likely to go into higher education, according to the OfS.
The situation is worse among the universities which ask for the highest entry grades, it says.
Currently, youngsters from the most advantaged areas of England are more than six times as likely as their less advantaged peers to go to one of the most selective institutions in the country, a new analysis by the OfS has found.
But if these universities meet tough new targets, which are meant to improve access to higher education, then this gulf will shrink over the next five years to less than four times as likely, the regulator has calculated.
OfS chairman Sir Michael Barber said: "The chance to go to university has been something of a postcode lottery, and I welcome the ambitious commitments universities are making to change this state of affairs."
"What is an assumed rite of passage for many young people across the country is often viewed very differently in rural and coastal communities, the industrial heartlands and military towns.
"The North-South divide crops up in many debates around equal opportunities, and higher education is no exception."
He added that in London, 54% of young people go into higher education, but in the north east of England it is 39% and in the south-west it is 37%.
"So this is more than a simple North-South divide," Sir Michael said. "In fact, the South West has the lowest participation rate of any region, while our most elite universities tend to recruit far fewer students from the West Midlands."
Under rules brought in when tuition fees were trebled to a maximum of £9,250 a year, institutions that want to charge the top rates must have access agreements signed off by the OfS.
These agreements contain targets on areas such as recruitment of particular under-represented groups, drop-out rates and gaps in degree achievement between students.
Individual agreements show the commitments universities have made.
For example, Oxford has pledged to cut the ratio of most-represented to least-represented groups from around 15 to one to eight to one, while Cambridge has committed to cutting the ratio from around 14 to one to around 6.7 to one.
Chris Millward, OfS director of fair access and participation, said: "There's a real issue about capitalising on the talents across all parts of the country.
"Nobody would say looking at the current profile of people going into the most selective universities that that reflects the talent and potential of students across the country.
"This is really about improving opportunity for people who could benefit from that kind of education and don't currently. And that's a fairness issue."
Mr Millward said that if universities do not meet their pledges, then the regulator will decide whether they have taken enough action to do so.
Universities found to have failed to improve access can face sanctions, including fines.
No institution has yet been fined for this reason.
Mr Millward also said the extent to which there could be "displacement" of more advantaged students will depend on whether universities decide to grow their numbers in order to help improve access.
"I would come back to this is about recognising talent from all backgrounds, and currently lots of students from the parts of the country that are beingtargeted now in these plans are not recognised," he said.
He said he understood that Oxford and Cambridge are not planning to increase their student numbers, adding: "Again it would be their own decision about whether they decide to do that.
"Some people have advocated that they should, but inevitably in Oxbridge if they don't grow, then the groups that are very highly represented in those universities will be less represented at the end of this. There's no doubt about that."
Mike Buchanan, executive director of HMC (the Headmasters' and Headmistresses' Conference), said: "We are confident that the exceptional results and soft skills that HMC schools provide will mean that our students will continue to get the university places they wish for in a competitive UK marketplace or at prestigious universities overseas.
"However, care is needed in starting actively to discriminate against individual young people on the basis of the class they were born into. The country needs all its young people to reach their potential if we are to create a bright new future for Britain post-Brexit.
"We urge the Government to enable universities and colleges to expand to take as many truly suitable students as necessary, rather than rob some students of a future to award it to others.
"Universities should also look at the increasing numbers of high-paying international students they are accepting, rather than deny places to UK students based on their class."