According to a survey by John Howson, a visiting professor at Oxford Brookes University and managing director of Education Data Surveys, there are 1,578 vacancies, a 5 per cent increase on last year.
Professor Howson said vacancies were set to soar further.
"The age profile of the teaching profession is such that many teachers will reach retirement age over the next decade," he said. "The number of deputy heads in the 35 to 45 age range is at a historic low, so finding new headteachers is going to be a challenge."
London schools are facing particular difficulties, even though some primaries in the city are offering heads' salaries of more than pound;60,000 a year.
A quarter of the London schools in the survey had been forced to readvertise their headteacher post this year after failing to make an appointment. Professor Howson said workload and tempting new posts on government initiatives were contributing to the dearth of potential school leaders.
And many more schools could soon find that they have heads under the age of 40.