The judicial review case involves a claim by three families that the government has failed to increase funding for high needs in line with rising demand.
It is the first time the government has been challenged in court over its funding of SEND services.
The funding gap - estimated to be £800m this year, rising to £1.6bn by 2021 - has left councils across the country unable to meet their statutory obligations to children who need extra educational support, the families claim.
The case comes as the National Education Union released findings showing that 8,587 children and young people with SEND are currently classed as "awaiting provision" for a school place, and have no access to any type of educational provision.
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According to Department for Education figures for January, the number of children and young people with an education, health and care plan (EHCP), who are waiting for provision, is more than double that recorded in 2017.
Lawyers for the three families argue that Education Secretary Damian Hinds and Chancellor Philip Hammond, acted unlawfully when deciding funds for complex SEND, when the budget was decided by Hammond in October 2018, and when Hinds decided to make £350m in "manifestly insufficient" extra funding available in December 2018.
"There is no evidence that the defendants have ever asked themselves whether SEN funding is sufficient to allow local authorities and schools to comply with their statutory duties and meet the needs of this particularly vulnerable cohort of children and young people, whereas all the evidence set out below and available to the defendants says that it is not," claims the legal document outlining the claimants' case.
The families, from North Yorkshire, Birmingham and East Sussex, are being supported by charities Mencap and the National Deaf Children's Society, as well as the campaign network SEND Action.
The families' lawyer Anne-Marie Irwin, of law firm Irwin Mitchell, said: "The issue of funding for special educational needs is...something that we have been contacted about on many occasions in recent years, but this is the first time that the government have been taken to court over its decisions on SEND funding.
"So many families are desperate to know that their children will be able to get the support they require to access an education, yet so many councils at the moment are resorting to budget cuts, which puts that under serious threat.
"Our clients in this case simply feel that enough is enough and want the government to reconsider the level of support it is providing to local authorities on the issue of special educational needs."
The three child claimants are Nico Heugh Simone, 15, from Robertsbridge, East Sussex, Benedict McFinnigan, 14, from Scarborough, North Yorkshire, and Dakota Riddell, nine, from Birmingham.
Nico has anxiety and other related conditions, meaning he needs special educational care to remain in mainstream school.
His family claims they have faced problems with East Sussex County Council refusing to meet the full cost of his requirements.
Benedict has post-traumatic stress disorder, anxiety, depression and chronic insomnia, but was initially refused an EHCP assessment by North Yorkshire County Council.
He has not been in mainstream school for around two years and is now attending a pupil referral unit for less than three hours a day.
Dakota has complex needs arising from conditions including cerebral palsy and global development delay. While her EHCP was drawn up in 2016, it is claimed that this was not updated for three years, despite changes in the level of support she requires.
The plan was eventually amended but her mother found it contained errors, and travel support which ensured Dakota could get to school has been withdrawn.
The four grounds of challenge, which are variously denied, are:
- A breach of the public sector equality duty, in that the defendants did not make proper inquiries about the gap between the cost of provision and the funding made available, and its impact on the right to education of children with SEN.
- A failure to promote the wellbeing of children, in breach of the Children and Young Persons Act.
- The defendants acted irrationally when deciding that the "solution to the problem lay in announcing an additional £350m and deferring the matter to the 2019 Spending Review".
- That the decision breached the right to education under Article 14 of the European Convention on Human Rights.
The case is scheduled to be heard at the High Court on 26-27 June.