BBC News: Privately educated UK graduates in high status jobs earn more than their state school counterparts, says a study.
The report, by the Sutton Trust and UpReach, examined those in careers such as law and financial services.
It found that, on average, three years after graduation, those who attended fee-paying schools earned £4,500 more.
The government said it was "determined... to ensure every child, regardless of background, reaches their potential" through its policies.
The report put the earnings gap down to factors such as the university attended, but also suggested non-academic factors, such as assertiveness, were at play.
The research also found salaries of the privately-educated increased more quickly, growing by £3,000 more over the same three-and-a-half year period.
Average salaries, six months after graduation, were more generous for those who had attended independent schools - £24,066 compared to £22,735, a difference of £1,331.
This difference rose to £4,450 after three years, with average salaries of £36,036 and £31,586 respectively.
The report - Private pay progression - says half of this difference can be explained by factors such as prior academic attainment and the type of university an individual attended.
But it says the remaining half cannot be explained by these factors and is likely to be down to non-academic factors such as articulacy, assertiveness and other important soft skills.
The research assessed jobs in the top national statistics socio-economic classification, including accountants, economists, solicitors, pharmacists, psychologists, higher education teachers and researchers, engineers and scientists, but excluding medics.
However, despite slower pay progression, the study found graduates without a private schooling were marginally more likely to remain in high status jobs.
The study found 71% of state-school educated graduates were still in such employment three-and-a-half years later, compared with 65% for their more privileged peers.
It says that while this difference is "only marginally statistically significant", it shows an ability to stay on and succeed.
"This suggests that once undergraduates from less privileged backgrounds access professional employment, they are more likely to stay and build a career within the professions," it says.
The report is calling on firms to identify graduates from less privileged backgrounds early on in the application process.
It says mentoring opportunities, career coaching and application guidance would all help improve non-academic skills.
Sir Peter Lampl, chairman of the Sutton Trust, said: "We know that graduates from less privileged backgrounds are under-represented in the top professions but today's research shows that they face disadvantage when it comes to pay progression too.
"This new research shows us how vital is it that firms do more to improve social mobility through their recruitment practices.
"Enabling greater access to a wider pool of diverse talent will deliver real benefits for employers and employees alike."
Henry Morris, founder of UpReach - an organisation which aims to help undergraduates from less-privileged backgrounds to land top jobs, said: "Today's research tells us that Britain's social mobility challenge does not end on a graduate's first day of work.
"Despite doing as well academically, the pay of graduates from more privileged backgrounds rises more quickly than their peers."
The findings come after accountancy firm Ernst and Young (EY) announced it is removing all academic and education details from its trainee application process.
EY will choose which applicants to interview based on their performance in online tests, in an attempt to improve workplace diversity.
The government said it was raising standards with "a rigorous new curriculum, world-class exams and a new accountability system that recognises the schools that equip every child with the skills and knowledge they need to succeed.
"At the same time our academies programme is transforming the lives of millions of pupils across the country and thanks to these reforms, one million more children are now being taught in good or outstanding schools than in 2010."