Private school head teachers in the UK say they are offering substitute family environments for children whose parents are working long hours.
More pupils have been joining independent sixth forms
The number of children being educated by members of the Independent Schools Council has remained steady despite a 5.9% rise in fees, its census shows.
The ISC, with more than four in every five fee-paying pupils, in almost 1,280 schools, says the sector is "thriving".
Fees for 441,758 day pupils and 67,335 boarders averaged £10,173 a year.
Class sizes were at a record low, with on average 9.7 children for every teacher.
More pupils in nurseries and sixth forms offset a small fall in those aged five to 16 - though that was less than the general decline in the number of young people.
PUPIL NUMBERS 2005-06
Age under 4: +624
Ages 5-10: -1,056
Ages 11-15: -570
Ages 16-19: +1,205
Source: ISC census, same 1,252 schools in both years
Overall, independent schools continue to account for just over 7% of the total school population.
Nigel Richardson, head of the Perse School, Cambridge, who chairs the Headmasters' and Headmistresses' Conference, one of the main independent school groups, said many hard-working parents liked the stability offered by a private education.
"With the pressures on them, it is very hard for a parent to devote large amounts of time every day of the week to their children.
"So we are providing something that in less complicated times families might have been better able to provide for themselves."
The ISC represents most of the larger independent schools, including 1,216 in England, 35 in Scotland, 17 in Wales and 10 in Northern Ireland.
'No university bias'
Head teachers believe the rise at sixth form level indicates a desire for specialist teaching that may not be available in the state sector, to boost students' university entrance chances.
People do not seem to have been deterred by talk of universities looking more favourably on pupils from disadvantaged backgrounds.
The census report says: "Extensive research from ISC indicates that there is no evidence of bias in the university application process."
The council said the 5.9% rise in fees was in line with inflation in the services sector (6.1% in January).
Salaries and pensions remained the largest expense, while capital spending on buildings and equipment totalled more than £700m in 2006, or £1,387 per pupil.
The ISC has changed the way it calculates average fees, to reflect the way different amounts are charged to pupils of different ages.
Thirty-two schools have fees of more than £8,000 per term
Overall average termly fees, as of January, were £3,391 on its new method compared with £3,714 on its old method, though it used the old methodology to calculate the year-on-year increase.
The number of pupils who received financial support from their school rose by several thousand, to very nearly a quarter of the total.
Commitments in Afghanistan and Iraq were thought to lie behind a 29% rise in the number of armed forces families sending their children to private schools, to 1,687 children.
There were 20,852 non-British pupils whose parents live overseas, with a 4.9% fall in the number of new students due almost entirely to a drop in the number from Hong Kong.
More came as a result of the growing wealth of China and the increasing popularity of UK education in Germany, the ISC said.
Rising middle classes in Russia and eastern Europe also fuelled continued increases.
The estimated value of overseas students to the economy rose from £322m to £356m - with many then staying on to go to university.