On the first day of its annual conference in Liverpool, the NEU has released analysis showing that just nine of the 150 local authorities in receipt of special educational needs and disabilities (SEND) funding had enough to support need in their area.
Some 94 per cent of local authorities have suffered shortfalls in their higher needs budgets - which they spend on SEND provision in schools.
During the same period - between 2015/16 and 2018/19 - the number of children and young people with education, health and care plans (EHCPs) rose by 33 per cent - from 240,000 to 320,000.
The union says that government investment in the "high needs block" rose, but only by six per cent - from £5.6bn to £6bn in today's prices - and therefore is not enough to support children with complex needs.
Hertfordshire County Council experienced the largest funding gap - £40m - of all the 150 local authorities in receipt of the funding.
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NEU joint general secretary Kevin Courtney said the funding shortfall for SEND provision comes against the backdrop of nine years of central government cuts to local authority budgets that had "left many councils on the brink".
"Between 2010 and 2020, councils will have lost almost 60p out of every £1 the government had provided for services," he said.
"This is an appalling way to be addressing the education of some of our most vulnerable children and young people and is causing untold misery and worry for thousands of families."
A total of six councils experienced a shortfall of more than £30m, the others being West Sussex County Council, Blackburn with Darwen Council, Manchester City Council, Hampshire County Council and Surrey County Council.
Five further councils reported a shortfall of between £20m and £30m, and 29 were short of between £10m and £20m.
NEU said one cause of the increase in demand for EHCPs was its extension to young people with additional needs aged 19 to 25, which came into force in February 2017.
Anntoinette Bramble, chair of the Local Government Association's children and young people board, said councils were reaching the point where money was "simply not there to keep up with demand, pushing support for children with SEND to a tipping point".
"While it was good the government announced money for SEND last year, it must use the forthcoming Spending Review to plug the estimated special needs funding gap facing councils of up to £1.6bn by 2021," she said.
Minister for children and families Nadhim Zahawi said the government had increased funding in recognition of the "challenges facing local authorities".
In December, the Department for Education announced an additional £250m of high needs funding for 2018/19 and 2019/20.
Councils are also getting an extra £100m to create more SEND places in mainstream schools, colleges and special schools.
The funding issue has for some time been highlighted by the sector, and the issue has also featured in the courts.
Surrey County Council is one of a handful of local authorities that faced a challenge over its cuts - a claim the High Court rejected in March.
However in August 2018, the High Court upheld campaigners' claims that the process used by Bristol City Council to cut SEND funding was legally flawed.
In June the High Court will consider further claims against SEND funding policies at North Yorkshire, Birmingham and East Sussex councils.