The surprising statistics, revealed at last week's conference of prep school heads, also came with the message that schools must "adapt or go under".
But the warning from chairman John Hawkins to the conference at Keele University may have been heeded already - the signs are that most prep schools are adapting very briskly to changing demand and that most of those likely to go under have already done so.
While the past few years have seen the merging of some schools that were struggling on their own, outright closures have slowed almost to a standstill. The 500-strong Incorporated Association of Preparatory Schools (IAPS) only registered the closure of one school last year.
The association heads gathered for their conference in a buoyant mood. What their schools offer - small classes, specialist teaching, good facilities and extended days - is what more and more parents want.
The most recent figures on pupil numbers from the Independent Schools Information Service (ISIS) show an increase of nearly 4 per cent in the seven to 11 age range and nearly 5 per cent at the pre-prep stage. They are in particular demand where state grammar schools remain, with a new generation of parents prepared to invest in the early years of education to boost their child's chances of good, free, secondary schooling.
What attracts parents also attracts teachers, even the male of the species. Prep schools have few problems with staff recruitment, as teachers respond to the lures of manageable children, higher pay and the chance to help out with team sports and other extra-curricular activities.
They attract graduate subject specialists to teach at key stage 2: ask a primary teacher what he or she does and the reply will be "I'm a primary teacher"; a prep school teacher's reply might be: "I'm a history teacher".
But the IAPS chairman voiced concern about future recruitment prospects, pointing out that the current sharp drop in applications for primary teacher training could have a serious effect on prep schools.
He urged a campaign to make sure that they continued to attract good, newly-qualified teachers.
But his greatest concern was the shortage of good applicants for headships. He urged heads to encourage their senior staff to take responsibility and training. He called for Government funding to encourage more teachers in the independent sector to take the National Professional Qualification for Headship.
The shortage of applications could be explained by the exposed position of prep school heads, David Hanson, the association's director of education, told The TES.
"It's the most vulnerable position in education," he said. "Unlike in the state sector, prep school heads do lose their jobs." About half a dozen association heads a year were sacked by their governors or proprietor, usually because of a difference in educational vision rather than because the head had made a mistake.