Hundreds of primary schools are struggling to recruit head teachers, according to a survey.
Increasing head teachers' salaries could make a difference
More than a third of primaries were unable to appoint after advertising between September 2006 and March, a study by Education Data Surveys says.
Too much pressure on head teachers, could be making the job less attractive, teachers' unions claim.
The government said the head teacher vacancy rate remained low but that it was aware that the job was challenging.
Some 2,388 primary schools and 2,957 secondaries and special schools advertised for a head teacher over the period.
Of these 683 primaries and 857 secondaries and special schools responded to the EDS survey.
The results suggested 35% of primary, 33% of special schools and 19% of secondaries failed to appoint following their advertisement.
These figures compare to the 28%, 30% and 22% respectively that reported the post was unfilled after the first advertisement the previous year.
The figures come from the 13th annual survey of the labour market for senior staff in schools across England and Wales, conducted by EDS and commissioned by the National Association of Head Teachers (NAHT) and the Association of School and College Leaders (ASCL).
NAHT general secretary Mick Brookes said the survey underlined the need for a review of the pressure on school leaders.
"If the government is to achieve its aim of raising standards and narrowing the achievement gap, it must throw its weight behind improving the attractiveness of leadership posts to ensure that school staff, children and young people have the strong and positive leadership they deserve."
Increase in salaries
Professor John Howson, of EDS, said the difference in wage between primary school teachers who take on extra responsibilities and head teachers is arguably too small to attract many candidates.
"The salary has to go up to attract the more marginal candidates to the job," he suggested.
Although the number of secondary schools that needed to advertise for a head teacher had decreased slightly for the second year running, the number that were not able to appoint was still too high, the survey noted.
ASCL general secretary John Dunford said: "School leaders salary and conditions must be commensurate with the high expectations now placed on them."
He added that the problem would get worse between 2008 and 2011 when a high number of head teachers were set to retire.
Schools minister Jim Knight the head teacher vacancy rate remained low and stable and actually fell in January 2007 to just 0.6%.
"But we are not at all complacent and we are well aware of the challenges around recruitment.
"Howson's work on advertisements can help us identify specific recruitment problems.
"I remain confident that we can ensure that school leadership is as effective as it can be in raising standards for all and is an attractive career option."
He said the government has increased the maximum heads can earn to over £100,000 a year and given schools record numbers of support staff to help heads in the "challenging" job they do.
Liberal Democrat education spokesman David Laws said: "These are horrific figures revealing a real crisis in school leadership.
"Effective leadership is absolutely vital for school success and the head teacher crisis is therefore likely to have a direct impact in the classroom and upon children's chances of success.
"Ministers have known about this problem but have failed to act. This report should act as a wake-up call."
Shadow schools minister Nick Gibb said the increase in paperwork for head teachers had put many teachers off the job.
"The desire of education bureaucrats to be all encompassing has created a pen pushing form filling nightmare for teachers and it needs to be minimised."
The government has a duty to set down to teachers the priorities from the public and from parents, but ministers shouldn't be providing a detailed blueprint for every minute of the day in the classroom."
The National College for School Leadership (NCSL) is spearheading a campaign to find the next generation of head teachers.
National succession consultants will work with local authorities, dioceses and other organisations to identify priorities and next steps to inspire potential head teachers and retain the skills and experience of heads already in the profession.