Teachers running Fresh Start schools, launching city academies or coaching groups of heads of failing schools through a recovery programme, should also be given far more time to carry out their challenging tasks.

The recommendations are contained in a report by Hay Management Consultants. It says these jobs cannot be done in a normal working day and compensation is needed in terms of pay and other benefits, such as a car, health insurance and pension enhancements.

Whereas such teachers can be dismissed with as little as three months’ notice, initial contracts of five years should be handed out to reflect the long-term nature of the job and to allow for deep-seated rather than “cosmetic” changes.

A TES survey found that only two out of 11 schools put under Fresh Start in the past year or two, improved their GCSE results.

The salary attached to thee high-profile posts should be increased from around pound;70,000 to up to pound;120,000, with possible bonuses of around pound;75,000 linked to successful completion of the job, the report says.

It also claims Fresh Start schools and city academies need a more knowledgeable governing team than “successful” schools and an entirely different framework of accountability.

David Hart, general secretary of the NAHT, said: “The report basically highlights that a great deal more thinking needs to be done at government level on how we are going to persuade successful heads to leave their schools and take up these challenging posts.

“There has been far too high a level of expectation in terms of the time it takes to turn around these schools. The Government has been looking for results far too quickly.

“You have also got to give heads very considerable management freedom in terms of recruiting and dismissing staff, exclusions and admissions and they need extremely good governing bodies.

“Finally, of course, a decent rewards package is essential,” Mr Hart added.