Richer and higher-achieving independent schools are giving a smaller proportion of their income in bursaries than less affluent schools, according to a report by the Sutton Trust and Staffordshire University.

They analysed the websites and accounts of 348 schools, finding that schools which devote 1-2 per cent of their income to bursaries have an average income of £10.4m, while those which give 6-8 per cent to bursaries have an average of £8.2m.

The report also states that, with the exception of very small schools, “the rate of bursary provision tends to decline with increasing school size and income”.

Meanwhile, the top 70 schools according to the Sunday Times’ league tables based on exam achievement spend an average of 4.3 per cent of their income on bursaries, while those ranked 211-280 give 7.2 per cent.

The report also singles out independent faith schools, as their average fee remission to help poorer students is nearly 10 per cent below the overall average.

Sir Peter Lampl, chair of the Sutton Trust, said that while bursaries levels have risen overall, progress is unevenly spread throughout the sector.

"It is concerning, for example, 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.

“While partnership and community work are important components of public benefit, bursary provision is perhaps the most effective way independent schools can boost social mobility."