That's why, in one of the roughest parts of London, a public schoolrecently built a little piece of Oxford -- a replica don's room -- in the hopes of boosting students' confidence when they go for an interview in the real thing. Two days a week, students from Brooke House Sixth Form College in Hackney, known as BSix, gather amid the room's leather-bound tomes, gilded picture frames and Chesterfield sofa to meet with an Oxford history tutor to prepare to apply to either Oxford or Cambridge.

BSix's students -- among the poorest in the U.K. -- will need all the help they can get. In wealthier parts of the country like Reading and Hammersmith, students in public schools are 50 times more likely to gain acceptance to Oxford or Cambridge than their counterparts in Hackney. They also face fierce competition from students armed with the best education money can buy: in 2010, Oxford offered 44% of its places to students from private schools, despite the fact that only 7% of British students attend them. The scales are weighted so heavily, in fact, that five British private schools sent more students to Oxford and Cambridge between 2007 and '09 than 2,000 public schools combined, according to the Sutton Trust, an educational charity in the U.K. And things don't appear to be changing quickly. In 2010-11, Britain's top 20 universities -- known as the Russell Group -- took proportionately fewer students from state-funded, public schools than the year before, according to the Higher Education Statistics Agency.

When it comes to race, the numbers are even more dire. A recent investigation by Parliament member David Lammy found that in 2009, only 27 black students were offered undergraduate places at all of Oxford's colleges combined. For the entire decade from 1999 to 2009, black students received 10 or fewer places at more than half of Oxford's undergraduate colleges. Merton College, which accepted 795 white students during that period, admitted just four black students. (The real tragedy, some would argue, is that in those 10 years, only 32 black students applied to the college.

Admissions are a subject that Britain's class warriors regularly clash over. Yet even the most hardened elitists would not deny that, historically, Oxford and Cambridge have served as a stopover for cosseted dauphins on their ascent from Britain's best schools to its halls of power. Every university-educated Prime Minister save Gordon Brown has attended either Oxford or Cambridge, and the tradition shows no sign of changing. Prime Minister David Cameron and his deputy, Nick Clegg, both attended top private schools and then Oxbridge, as did almost 40% of their Cabinet. Labour leader Ed Miliband also attended Cambridge, though he did not attend a private secondary school. It's not just politicians. All but one of the judges sitting on the U.K.'s Supreme Court and 81% of the current senior judiciary in the country studied at one of the two storied universities. Of the leading British journalists who went to university, more than half were educated at Oxford or Cambridge, according to a 2007 study by the Sutton Trust.

The cabinet's privileged pedigree hasn't prevented its leaders from trying to address the problem, however. Last month, the government announced a record £900 million ($1.46 billion) budget for outreach to disadvantaged students, a total that has grown by $162 million in the past three years. And in late February, the government made the controversial decision to appoint Les Ebdon, vice chancellor of the University of Bedfordshire, as director of the Office for Fair Access. Ebdon's suggestion that the government withhold some funding for universities that fail to admit more poor students sparked a middle-class firestorm. The Sunday Times of London splashed the headline "Will This Man Stop Your Child Going to a Top University?" across an unflattering picture of Ebdon superimposed over an idyllic Cambridge college. In the photo, Ebdon holds a sign reading, "Please Keep Out -- Unless from a Disadvantaged Group, as Approved by the Dept. Social Engineering."

Meanwhile, Oxford, which would rather the government not fiddle with its admissions policies, has pursued its own reform agenda. The university now spends $4 million a year on student outreach, which includes school visits and teacher-training sessions aimed at encouraging poor and minority students to apply to the university. In 2010, Oxford also launched a summer school called UNIQ, which gives some 500 academically talented, state-school students a chance to experience studying at Oxford for a week. In addition, the university admissions office highly recommends to tutors that qualified students from poor areas be invited for interviews. And it has set of a target of increasing the number of undergrads from socioeconomically disadvantaged areas from 6.1% to 9% by 2016-17.

Still, the university balks at the idea of admitting a student with lower grades just because of his or her socioeconomic background. "If your education is based around one-on-one tutorials with leading academics, you've got to select people who are really bright and will respond to that sort of educational system," says Oxford press officer Julia Paolitto. British parents paying through the nose for private schooling to ensure their children's places at Oxbridge tend to agree. But even those working in inner-city public schools say putting too much weight on a student's background may not be a good idea. "We don't want any concessions from anybody," says Ken Warman, principal of BSix. "It's not a good message for our students. Would you be as confident if you were let in because of where you were from?"

One thing everyone seems to agree on is the need for more bright disadvantaged students to apply. And in that area, there's a lot to do. According to the Sutton Trust, less than half of public-school teachers urge their most promising students to consider Oxford and Cambridge. "There is an awful lot of mythology about what it is and isn't to become a student at Oxford," says Mike Nicholson, director of undergraduate admissions at Oxford. "We now spend a lot of time challenging that mythology."

For one student in Hackney, this has worked. In 2008, 16-year-old Allun Bokhari arrived at BSix having dropped out of his previous school, with no academic qualifications. At first glance, he hardly seemed like Oxbridge material. Yet his teachers quickly spotted that he was smart and began helping him preparing for the tests that Oxford requires. Two years later, Bokhari was accepted to study history and politics at Queen's College, Oxford. In 2011, BSix sent a student to Cambridge, bringing the school's Oxbridge total to two. Warman says it may not seem like many, but looks can be deceiving. "For a college like ours, that's a big breakthrough."