Oxford’s intake displayed a geographic imbalance between the north of Britain and the more affluent south, where the bulk of national wealth is concentrated.

“Oxford reflects the inequalities — socio-economic, ethnic and regional — that exist in British society,” Louise Richardson, the university’s vice chancellor, said in a foreword to the report.

“The picture that emerges,” she said, “is of a university which is changing: evolving fast for an institution of its age and standing, but perhaps too slowly to meet public expectations. It is a picture of progress on a great many fronts, but with work remaining to be done.”

In a section titled Key Points, the report focused on progress in admissions, including “more women admitted than men in 2017” and higher proportions of undergraduate admissions among groups that were traditionally disadvantaged.

Yet, according to the Cherwell article, “17 of the top 20 schools for Oxford admissions in 2017 are fee-paying, while the other three are prestigious grammar schools.” Additionally, the newspaper said, state-educated students tended to apply to the most oversubscribed subjects, lowering their prospects, while applicants from private schools tended to apply to less sought-after courses, such as classics or modern languages.

At the heart of the debate is a perceived contest between demographics and academic excellence. Critics such as Mr. Lammy, the Labour lawmaker, argue that a student from a low-income area who gets good grades on the national A-level exams at the end of high school “is more talented than their contemporary with the same grades” at a top fee-paying school such as Eton or Harrow. “And all the academic evidence shows that they far outshine their peers at university, too,” he said.

“If you’re on the 20th floor of a tower block estate and you’re getting straight As,” Mr. Lammy told the BBC, “you apply, go for a difficult interview,” and then, he added, if the application is unsuccessful, “none of the other kids apply the following year.”