This is according to research commissioned the National Association of Head Teachers (NAHT). The 16th annual survey of the education labour market, prepared by Education Data Surveys (EDS), showed a significant increase in the percentage of headship posts remaining unfilled after the first advertisement.
Containing the details of 1,499 posts on the Leadership Scale, the study found that a third of head teacher vacancies advertised between September 2009 and the end of April 2010 by publicly-funded schools and academies in England and Wales were unfilled after first being promoted. This compares to just 26 per cent in 2008/09.
Some 34 per cent of primary schools reported having a position unfilled after advertising, up from 26 per cent the year previously. One in five secondary schools experienced this problem, a rise of one per cent.
The figures are even worse for special needs schools, with 43 per cent of such education institutions failing to fill an advertised head teacher position during 2009/10, compared to 27 per cent during 2008/09.
According to the NAHT, struggling to fill positions causes extra uncertainty for staff, pupils and parents and difficulties for succession planning.
Schools with high re-advertisement rates also often face significant additional expenditure in order to recruit a suitable candidate, the union argued.
The NAHT also warned that an increase in the number of head teachers retiring would lead to further issues with recruiting sufficient suitably-qualified candidates.
However, the NAHT figures also show that around 4.6 people applied for every head teacher post in primary schools, down from 4.8 the previous years. Leadership roles in secondary schools attracted even more candidates, with 13.6 people on average applying for each role. Yet, only 2.6 applicants were interviewed for primary headships, down from 2.7 last year, while five people were interviewed for a similar position in a secondary school.
Russell Hobby, General Secretary of the NAHT, said the report highlights that it is essential for everyone within the education sector to promote the role of school leadership.
"To encourage the leaders of tomorrow we need to give leaders today freedom and autonomy under fair and accurate accountability in order to flourish in what, on a good day, is the best job in the world," he stated.
Professor John Howson of Education Data Surveys at TSL Education said he was concerned that the new arrangements for the mandatory National Professional Qualification for Headship (NPQH) qualification have not yet solved the problem of head teacher recruitment.
Under the rules which came into force in April 2004, anyone who is appointed to their first headship post in the local education authority-maintained sector, including nursery schools, have to hold the NPQH or be working towards it.
Christine Blower, General Secretary of the National Union of Teachers, dismissed suggestions that the need for a NPQH is hindering applicants.
Instead, she argued that the responsibilities of being a head teacher may be playing a key role in why more people are not applying for such positions.
"We don't take the view that the need for a qualification is the major difficulty. It is simply that the job of being a head teacher is extremely burdensome, and many people entering teaching do not consider that they can maintain any work-life balance and also fulfil the role of head teacher," she stated.
According to Teacher Net, head teachers are typically responsible for ensuring that all staff understand the school's policy and their own responsibilities. They also need to make sure that staff training is arranged as necessary and that parents are kept informed regarding the school and their children.
Heads also need to ensure that regular reports are made to governing bodies, manage suspensions and maintain the smooth day-to-day running of the school. They also need to establish a method of contacting the police in the event of emergency and, in some cases, teach classes.
Teachers in a leadership position also play a key role in ensuring children achieve their potential, the NAHT said.
Mr Hobby concluded: "You can't have great schools without great school leadership."