One in five schools which advertised for a head teacher last year failed to find a suitable one, a study says.
More women are appointed to headships at primary level
Head teachers' leaders are warning that recruitment of heads is becoming more difficult every year.
The situation was worst in the primary sector, where 28% of heads' vacancies were not filled. The figure in secondary schools was 20%.
The study of vacancies in England and Wales in the year to July was carried out by Education Data Surveys.
It was commission by the National Association of Head Teachers (NAHT) and the Secondary Heads Association (SHA).
Researchers found that the number of people applying for vacancies in all types of school was lower than last year.
On average, about 13 people applied for each position as a secondary school head, while primary school head teacher vacancies attracted just over five applicants.
Risk and reward
John Dunford, general secretary of SHA, said people were put off from applying by the range of responsibilities, over-accountability and the rate of education reform.
"The survey shows clearly that recruitment to school headship is becoming more difficult every year," he said.
"Yet school leadership remains the most rewarding of jobs in the influence that it can have over the lives of young people. We must not discourage the best teachers from applying."
NAHT general secretary Mick Brookes said: "If the successes of the education system are to be sustained, schools must be able to attract the brightest and best into school leadership.
"Risk, responsibility and reward must be brought into balance."
Researchers noted a shift towards more women being appointed to leadership roles in secondary schools. A total of 39% of those appointed to headships were women, while the figure was 51% among new assistant heads.
In primary schools, the majority (70%) of leadership posts were awarded to women.
Few headship appointments were made to people who were not white, researchers said, although there had been a slight improvement in the ethnic balance at assistant head level.
However researchers did not have information about the ethnic backgrounds of all applicants, only of those appointed.