Chris Woodhead has declared war on "weak" schools as he tries to expand his private education empire.
The former chief inspector, now chairman of Cognita, which owns 20 private schools, told a conference of almost 100 private-school headteachers that they had to maintain the highest standards or risk being forced out of business.
His comments follow warnings by Joe Peake, chairman of the Society of Headmasters and Headmistresses of Independent Schools, that the rise of companies such as Cognita and Global Education Management Systems (GEMS) posed a unique threat to the private sector.
Heads are concerned that smaller, established independent schools may be undercut by profit-making businesses, which can tempt parents with lower fees.
Mr Peake, head of the pound;9,100-a-year St George's college in Surrey, said: "Could we compete with their lower overheads and centralised administration? They could certainly offer the diversity and choice, which the Government says it wants, and want to do it for pound;6,000-a-year.
These are questions few governing bodies can afford to ignore."
GEMS and Cognita are the biggest profit-making owners of private schools in the UK, although not-for-profit organisations such as the Girls' Day School Trust and the United Church Schools Trust are established names in the mass-ownership market.
Cognita, which is backed by a pound;500 million private equity fund, runs private schools across England, and has bought 17 schools from Asquith Court, the nursery care provider. It hopes to have 24 or more in the next two years. GEMS, backed by the Dubai millionaire Sunny Varkey, has 13 schools and has set aside pound;190m to expand its UK empire.
Mr Peake, addressing the SHMIS conference in York, estimated that the number of private- school pupils would drop by 8 per cent in the next 15 years because of falling birth rates. And he said there were concerns that Cognita and GEMS were buying into "an already saturated market" at the worst possible time.
But Professor Woodhead, who unveiled plans last month for a new no-nonsense teacher-training course which cuts out all "politically correct" educational theory, said demand was rising and disaffection with state schools would force more parents to go private.
Professor Woodhead forecast that within 10 years the Government would introduce vouchers, offering parents a private education for the same price as the cost of a state place. But he admitted that competition from Cognita and GEMS could force some schools out of business.
"Clearly any school that is weak, and by that I mean not giving parents what they want, will be under threat from a market that is increasingly competitive," he said.
Hugh MacPherson, GEMS' chief operating officer, told delegates:
"Competition is healthy and should shake out the weak and remove establishments that are less effective."