Rich, large independent schools give less of their income for bursaries than smaller, poorer ones, a study suggests.
Schools with higher incomes and further up league tables gave proportionally less for poorer pupils' places, the study funded by the Sutton Trust said.
But the Independent Schools Council said the study of 348 schools in England was flawed and no link existed.
Independent schools must show they provide "public benefit" to maintain their charity status.
The study, by Staffordshire University, examined the financial accounts and information on the websites of the schools.
Researchers said they had concluded that:
- Schools devoted, on average, 7.8% of their income to bursaries and scholarships, up from 6.6% in 2000
- More prestigious schools tended to devote a lower proportion of their income to scholarships and bursaries - with those in The Times' top 70 offering 4.3% of their income, compared to 7.2% by those ranked 211 to 280
- Except for very small schools, the rate of bursary provision tended to decline with increasing school size and income
- Independent faith schools tended to offer less of their income for bursaries and scholarships than non-faith schools
- Only half of independent schools disclosed in their annual accounts the proportion of income set aside for bursaries, and most did not publish on their websites the criteria for awarding bursaries
Sir Peter Lampl, chairman of the Sutton Trust, a leading educational charity, welcomed the rise in funding for bursaries.
But he pointed out that half the money for subsidised places is used for scholarships which are not means tested and said progress on the issue was uneven.
"It is concerning... that the most prestigious private schools - which offer their pupils exceptional life chances - appear, on average, to be doing less to widen access than their lower-attaining counterparts," he said.
The ISC, which represents 1,260 independent schools in the UK, said the Sutton Trust's research was based on "out of date, incomplete and mismatched data".
It said its own unpublished analysis, using a larger sample and more recent information, "found no correlation between bursaries and a school's ranking or revenue".
The Sutton Trust had failed to take into account whether a school had income from endowments and how much it cost to run the school, the ISC said.
Much of the data used by the ISC is not public.
Independent schools have been criticised for not being more open about their bursary policies and the funds they offer for them.
The research comes as independent schools are pressing for more clarity from the Charities Commission on what is meant by "public benefit".
The ISC is pushing for a judicial review of the Charities Commission's guidance.
It says the Sutton Trust and Charities Commission are making an "error" in "rating bursaries as the key to public benefit and social mobility".
The ISC says one in three independent school students receive help with their fees, and says bursaries are "extremely costly" and make it harder to keep fees low and thus widen participation.