The education secretary has pledged to make the “strongest case” for school funding ahead of the spending review after headteachers said an extra £5.7bn was needed to stop cash-strapped schools shutting down.

Damian Hinds told more than 1,000 school leaders he has heard them “loud and clear” and will call for more investment by highlighting the “moral argument” as well the potential benefits to the economy.

The minister’s address to the Association of School and College Leaders (ASCL) annual conference in Birmingham came as heads warned that more schools could face insolvency unless funding improves.

A group of parents also gathered outside the conference venue with banners and megaphones to call on Mr Hinds to urgently invest more money in schools to ensure the most vulnerable families were not hit.

Funding experts for ASCL have estimated a shortfall of £5.7bn in the amount needed by primary and secondary schools in England in 2019-20 to give every child the education they deserve.

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Many schools have had to reduce staffing, which means more classes of more than 30 children, less one-to-one support for pupils and cuts to the curriculum, the headteachers’ union warned.

Headteacher Richard Sheriff, president of ASCL, told conference attendees: “On the current trajectory, schools will either have to make more unpalatable cuts to the curriculum and the support they provide to pupils or they will face insolvency.

“This is not a scenario which is acceptable to anyone – schools, parents, communities or government.”

Lucy Bassatt, one of the parents protesting outside the conference venue, said the systemic funding cuts make her “want to cry”. She added: “Schools are talking about turning the lights off to save money.”

It is understood that more than 15 schools in Birmingham have already introduced, or are looking to introduce, a four-and-a-half-day week.

Ms Bassatt, who is a parent at a Birmingham school that is consulting over shortening the school week, said: “I am concerned that my employer might not be willing for me to take Friday off or a half day and that will affect my income by thousands a year.”

Lisa Hebrard, from campaign group Save our Schools West Midlands, said parents have been sent “begging letters” from heads who have asked them to help pay for school books, pens and glue sticks.

She added: “It is the government’s responsibility. How can the schools do it without the money? They are trying their best.”

Mr Hinds said: “I have heard the message on funding loud and clear, and before I go any further, I want to address it directly.

“I understand the real concerns on funding, I get that finances are challenging for schools and that many of you have had to make and are having to make very hard choices.

“I know that rising costs from suppliers to supply agencies add to these pressures, alongside the particular pressures in high needs.”

Parents protest outside the ASCL conference (Vicki Westwood) (Save Our Schools West Midlands)

He told heads he would use the spending review to make the “strongest possible case” for education.