The number of children attending independent schools has increased slightly, in contrast with a decline in pupil rolls in the state sector.
Independent school fees rose by three times the rate of inflation
The Independent Schools Council said pupil numbers were up by 1,359 to 505,450 since last year.
This brings the increase in England and Scotland since 2001 to 13,508 (2.7%). The total pupil roll, including state schools, has fallen by 103,173 (1.4%).
But private school fees are rising by three times the rate of inflation.
Parents paid £3,456 a term on average during 2005-06 - 5.7% more than the previous year.
This is three times the current 1.9% UK rate of inflation, but the lowest fees increase since 1999.
The ISC said most of the money had gone on extra staff costs.
The rise in pupil numbers follows an overall decline of about 3,000 in last year's ISC census.
The latest increase is mostly accounted for by 870 more children coming from abroad.
ISC general secretary Jonathan Shephard said: "The health of the sector is a reflection of the parental demand for the broad curriculum, small class sizes, excellent teaching, extra-curricular activities and added value that the independent sector provides."
The average class size fell from 9.98 children per teacher to 9.87.
Mr Shepherd said: "The sector is now educating more children than at the peak of the Assisted Places Scheme in 1998 when it helped the parents of 40,331 pupils."
ISC figures show that 93.1% of sixth-form leavers went on to higher education in 2005-06.
Its 1,272 member schools contained 68,409 boarders and 437,041 day pupils.