The cost of sending a child to a private school is rising around four times faster than earnings, according to research.
The study suggests that some parents are increasingly unable to afford to educate their children privately, with average fees now taking up more than a third of the average full-time salary.
Independent-school leaders reacted to the news, saying schools were doing everything they could to keep fees low and support parents with bursaries.
Some schools have been forced to make life easier for parents by allowing them to pay in monthly instalments or by providing loans to pay fees.
And Hipperholme Grammar School in Halifax this week announced it was planning to cut its fees by 10 per cent by September next year because parents were struggling to pay.
But these measures have not prevented a stream of high-profile independent-school closures in recent years, and a number of private schools have converted to state-funded free school status in a bid to stay afloat.
The research, by Lloyds Bank, found average fees for a pupil attending a private day school now stand at around £12,345, up 21 per cent from £10,176 in 2009.
At the same time, earnings for a full-time employee have risen by around 5 per cent, Lloyds concluded.
The study found that private-school fees have increased as a proportion of estimated earnings, suggesting that the current average school cost of £12,345 is equivalent to 37 per cent of annual average gross full-time earnings of around £33,693.
The bank's analysis found variations around the country, with the highest fees seen in Greater London, at £14,544 a year on average.
In the north, they stand at £9,984 and Scottish schools charge an average of £10,431.
Just over a third of private-school pupils receive financial help with the cost of their education, Lloyds concluded, with the average value of this support standing at nearly £4,687.
Matthew Burgess, general secretary of the Independent Schools Council, said: "Independent schools receive no state support for the world-class education they provide. The vast majority are not-for-profit educational charities and must look to fee-paying parents as their sole source of funding.
"Independent schools also increasingly subsidise the cost of their service for low-waged parents: bursaries funded by the sector now provide the same number of places as under the former assisted places scheme and are valued at more than £660 million annually."