Teachers’ leaders are calling on the government to fund an immediate 5% pay rise for teaching staff in an attempt to fend off a growing recruitment and retention crisis in schools.

In a letter to the education secretary, Justine Greening, ahead of the autumn budget, leaders of the main education unions say teacher pay is lagging significantly behind that of other graduate professions, leading to teacher supply problems.

Echoing earlier warnings by the School Teachers’ Review Body (STRB), which makes recommendations to ministers about teacher pay, the letter describes the situation as critical and says it represents “a substantial risk to the functioning of an effective education system”.

Teacher salaries have been held down for the past seven years by a pay cap that has also suppressed pay among NHS and other public sector workers. They will all be lobbying the chancellor with equal vigour for more money in the budget this month.

In a joint letter, the Association of School and College Leaders, the National Association of Head Teachers, the National Education Union, UCAC and Voice argue that after seven years of real-terms pay cuts, teacher pay is no longer competitive in a strong labour market with increasing opportunities for graduates.

“No education system can exceed the quality of its teachers,” the letter notes. “In England we are failing to recruit sufficient trainee teachers, particularly in the EBacc subjects which the government requires schools in England to offer to the majority of their pupils.”

It says flagging pay and high levels of accountability are deterring teachers and middle leaders from applying for headships and driving out many already in the profession.

“The situation is now so critical that it requires firm and decisive action,” the letter says. “In order to support and secure recruitment and retention, teachers’ pay levels must be restored at least to the levels that existed before the start of pay restraint in 2010. We believe that teachers must be given an immediate pay rise of 5% in 2018 as a step towards this.”

Teachers’ hopes for a pay rise were boosted fractionally in September when Liz Truss, the chief secretary to the Treasury, wrote to the STRB stating that skills shortages in some areas meant the government was prepared to accept a pay rise above the 1% limit for 2018-19.

Unions welcomed the move but said the government would have to provide extra funding to support teacher pay rises, otherwise money would be taken from elsewhere in schools’ already over-stretched budgets.

The government has pledged to give schools an additional £1.3bn, some of which will come from other departmental savings, but unions say it is not enough to keep up with the cost pressures on school budgets.