Professor John Howson said the findings from his annual survey of headteacher job adverts are the worst since his research company Education Data Systems began the study 21 years ago.
More than 2,600 schools in England and Wales needed to advertise for a head last year, and at least 1,000 had to readvertise.
The proportion of posts being readvertised increased between 2004 and 2005 from 27 per cent to 36 per cent in secondaries and 37 to 38 per cent in primaries.
Professor Howson said: "The level of readvertisement clearly demonstrates a market in some form of crisis. Schools that do not have a permanent head will have problems developing their policies. Their parents may drift to a more settled school and their pupils' education will be affected."
Faith schools and those in the capital were, as in previous years, the worst affected. Nearly 59 per cent of inner-London schools that advertised had to repeat the exercise, as did 44 per cent of Church of England schools and 59 per cent of Roman Catholic schools.
Professor Howson said the age profile of the profession was to blame. Large numbers of heads are reaching retirement age and this will peak in 2008.
Some governing bodies did not offer high enough salaries the first time round.
Secondary headteacher salaries of more than pound;100,000 per year are becoming increasingly common, even outside London.
Primary heads are catching up. Wembley Manor school in Middlesex, has advertised a salary of pound;90,000 a year, and Colegrave school in Newham, is today offering a salary of more than pound;80,000 for its next head.
Professor Howson said the gap between pay for experienced teachers and members of school leadership teams remained too narrow, giving staff little incentive to seek promotion.
The Government and the School Teachers' Review Body are due to commission a study this year into the roles and salaries of school leaders.
John Dunford, general secondary of the Association of School and College Leaders, said the figures indicated that headteacher recruitment was "moving from a worrying situation to a crisis".
Mick Brookes, general secretary of the National Association of Head Teachers, said teachers saw a head's job as high-risk and overloaded with initiatives.
New academies also had problems in finding heads. A handful had to readvertise, including the Oasis academy, due to open in Enfield, north London, next year.
Dr Patrick White, a sociology lecturer at Leicester university, urged caution over the figures. "Job advertisements are an indicator, but several previous claims about a recruitment crisis in education have proven unfounded so we should investigate further before panicking," he said.
A DfES spokesman said that the number of schools without a permanent headteacher had fallen from 261 in 1998 to 190 this year. "A tally of advertisements placed in newspapers is not an accurate reflection of the situation in our schools," he said. "No school will be without a head. If a full-time, permanent post has not yet been filled, then there will be a temporary or acting head in place."