Fees have risen by an average 6%, the Independent Schools Council said
The number of pupils in the UK being taught in private schools rose by about 3,000 last year to 514,531, according to a major annual survey.
The numbers were down by 103 when comparing only schools that were in the annual census in both 2008 and 2009.
The Independent Schools Council (ISC) said the private school sector was weathering the recession.
Fees went up by almost 6%, capital spending by 15% and the number of boarders went up by more than 1,000.
ISC members, covering the eight major private schools' associations, educate more than half a million children in 1,265 schools.
There is a total of about 2,600 schools in the whole independent sector in the UK.
The schools range in size from fewer than 50 pupils to more than 2,300.
The census report said: "As economic conditions tighten, the average school size may well rise as schools seek to gain economies of scale and this may be evidenced by increased merger activity."
The year-on-year comparisons relate to 1,240 schools that responded to the census in both 2008 and 2009.
On that basis pupil numbers totalled 508,678 in 2009 compared with 508,781 the year before, a fall of 103.
The number of students aged 11 was up by 1.91% and there were 2.95% more aged 14.
Boarding numbers rose from 67,046 in 2008 to 68,131 - the biggest rise for six years.
ISC chief executive David Lyscom said the schools were "a UK success story".
"Our annual census gives clear evidence that pupil numbers are holding up in 2009 despite the economic gloom. Heads tell us that parent interest in places for next year remains high.
"The reasons are clear. According to the OECD Pisa study our schools offer the best education globally, and we attract increasing numbers from overseas."
With just over half of A-level entries by ISC pupils awarded a grade A last summer, 93% of school leavers went in to higher education compared with 92.9% in 2008.
Fees went up by 5.9% to an average of £4,034 per term, ranging from less than £900 to more than £9,000.
About a third of pupils, 168,564, received assistance with fees, up 6.08% on 2008. Nearly 80% of these had financial help from their schools.
The ISC said fears of redundancies among parents in the recession, affecting demand for private school places, was not as bad as some thought.
Many parents worked in sectors that had not seen many layoffs, and about a quarter were in the public sector.
Mr Lyscom said: "We do not foresee a collapse and a catastrophe, I think we will be able to manage whatever comes down the road."
The schools say they have seen a continued rise in the number of so-called flexi-boarders, whose parents are both working long hours and are willing to pay schools to cover for them.
The chair of the Independent Association of Prep Schools, Diana Watkins, said: "We are noticing more and more parents, who if they have got jobs are working longer hours, who are holding on to their jobs, and perhaps both parents working longer hours.
"The knock-on effect to us is that we are getting far more flexi-boarders of people who are staying later into school."
Schools' capital spending was up 15%.
The long lead times for major building and renovation works meant that decisions would have been taken well ahead of the recession.
There was a small increase in staffing levels, further reducing the teacher-pupil ratio to just over one to 11.
For the first time the ISC asked about the ethnic background of pupils.
Results from about 75% of the schools showed some 78% were white British and 21% were from a minority ethnic background, compared with 85% and 14% in state schools.