A teaching union has accused the government of making “empty promises” to the families of one million children diagnosed with special educational needs whose schools have failed to receive additional funding.

The National Association of Head Teachers (NAHT) said funding for schools supporting pupils with special needs and disabilities was at crisis point, citing a survey of members that found 94% said it was harder to support such pupils now than two years ago.

“The picture facing schools supporting children with special educational needs is bleak. Not only are school budgets at breaking point, there have been severe cuts to health and social care provision,” said Paul Whiteman, the NAHT’s general secretary.

“Schools are left struggling to meet the needs of our most vulnerable pupils. Without sufficient funding and a more coherent approach, the special education needs code of practice is nothing more than an empty promise from government to parents and children.”

The union concludes in a report that the Department for Education must undertake a full review of demand for high-needs funding and secure an immediate increase from the Treasury.

The report includes contributions from school leaders, including one who said: “A child arrived in September in a wheelchair with cerebral palsy. We have to provide one-to-one support and two-to-one for toileting. We have received not a penny. Applied for top-up funding, still waiting eight months later.”

The survey found that 83% of respondents had not received any funding from health and social care budgets to support pupils with special needs statements or individual education health and care plans.

Schools face long waits even to receive a diagnosis or report, with a substantial number of heads reporting waits of more than six months from referral for a health and care assessment to be completed.

Nadhim Zahawi, the minister for children and families, said the government recognised the increasing pressure on schools and high-needs budgets, and argued that funding was rising in response.

“We have undertaken the biggest special educational needs reforms in a generation, including the introduction of education health and care plans, so that support is tailored to the needs of individuals and families are put at the heart of the process,” Zahawi said.

Whiteman said mainstream schools that admitted pupils with special needs and disabilities were being penalised by the poor levels of funding. Around 1.28 million children are recognised as having special educational needs, and Whiteman said a million of them appeared to have received no additional funding through their schools.

“The financial burden of additional support penalises those mainstream schools that are the most inclusive. This is unsustainable,” he said. “Schools are seriously struggling to fund special needs support in the face of crippling budget pressures that sees them forced to cut critical support staff. We urgently need the government to recognise the scale of the problem and to secure an immediate increase in funding from the Treasury. It is make or break time for school funding.”

Anntoinette Bramble, chair of the Local Government Association’s children and young people board, said the report reinforced the desperate need for the government to improve funding.

“As a starting point we are calling for an urgent review of funding to meet the unprecedented rise in demand that councils are experiencing,” she said.