US Edition Cheltenham Ladies' College will charge £9,578 per term for sixth form boarders joining in September.
Eton, Winchester and Wycombe Abbey will also charge over £9,000 a term.
Janette Wallis, of the Good Schools Guide, said: "If this pattern continues, next year we will see the previously unthinkable - the £10,000-a-term boarding school fee.
"It seems some schools see themselves as entirely immune from the ups and downs of the economy. But our experience shows schools are underestimating parents' sensitivities to fee increases."
All bar one of England's top 20 private schools have raised their fees above inflation.
St Paul's Girls' School is leading the pack with a rise of more than 14 per cent to £5,204 for day students.
Clarissa Farr, high mistress of St Paul's Girls', said: "The real cost in the last two years is greater, due mainly to smaller class sizes.
"Maintaining attractive salaries is important to maintain our standards."
Despite topping the fees table Vicky Tuck, principal of Cheltenham Ladies' College, said the school was "mindful of the credit crunch".
The college raised fees by a below average 4 per cent. "We have had to trim various things to keep fee increases at that level," she said.
The City of London School for boys is the only top 20 school to keep fee increases below inflation, with a rise of just 2 per cent.
The school, which lies within the Square Mile, educates many bankers' children.
According to research by the Halifax, parents in only 13 occupations can now afford to send their children to private schools, with teachers, engineers, police officers and even some doctors priced out of the market.
Rob Roy, of MTM education consultancy, said: "A third of families will be hit considerably by the rises. They will look to cut back on all kinds of expenditure - eating out, holidays, gyms, cars - before they get to fees." As many as 18,000 parents took out personal loans to pay for school fees last year. The average loan was £9,065, with experts claiming applications will rise further as parents struggle with rising energy, fuel and food bills.
According to the Sainsbury's Finance report, 18,000 UK loans worth an estimated £165 million were taken out last year to cover school fees.