Children with special educational needs and disabilities (SEND) are being failed by a system “on the verge of crisis” as demand for specialist support soars and threatens to bankrupt local authorities, a Guardian investigation has revealed.

Parents of children with SEND are increasingly locked in prolonged and costly disputes with councils across England who are too often failing to deliver on their legal obligations.

As a result, many of the most vulnerable children in society end up without the support to which they are entitled, and are out of school for months – even years – as parents battle to secure the right provision to meet their child’s needs.

Appeals heard by the special educational needs and disability tribunal have nearly doubled in the past two years. According to the most recent figures, parents are successful in 89% of tribunal hearings, prompting concerns that some local authorities are making poor decisions, delaying vulnerable children’s access to education.

Between 2011-12 and 2015-16, the tribunal heard about 800 cases a year; in 2016-17 the number rose to 1,600 in the fallout after sweeping government changes for children with SEN and disabilities that came into force in 2014.

Ali Fiddy, the chief executive of Independent Parental Special Education Advice (IPSEA), which offers advice and support for parents, said there had been a 56% increase in demand for IPSEA’s services since the Children and Families Act 2014 which they were struggling to meet.

“The system for supporting children and young people with SEND is verging on crisis. Against a backdrop of increasing cuts to local authority budgets, parents are having to deal with poor decision making on the part of local authorities which frequently stems from a lack of understanding of the legal framework.”

Findings by the local government and social care ombudsman, who investigates complaints about local public services, confirm worrying levels of council failure within the SEND system. Out of 200 investigations into parents’ complaints, the ombudsman, Michael King, found in favour of parents in eight out of 10 cases.

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One family had to go to tribunal twice and the ombudsman on three separate occasions to fight for the right provision for their 11-year-old son. “As a family it has a huge cost, both emotionally and financially. They failed him consistently for three years,” the mother said. “It’s left me feeling quite bruised and scared that the people who are supposed to be looking out for children are not.”

King said: “While our investigations can only provide part of the picture of how the SEN system is functioning – that picture is causing concern. The reality is that some families are suffering a disproportionate burden in having to battle for the support their children are entitled to.”

More than 1.2 million school pupils – about 15% of all those in England – have some kind of SEND, according to the Department for Education. Approximately 253,000 (3% of all pupils) have SEND statements or education and health care plans (EHCP), a legally binding document detailing the additional support that child needs.

Councils, suffering from years of budget cuts, warn the current system is “unsustainable”. The Association of Directors of Children’s Services (ADCS) said 68 out of 85 local authorities who responded to a survey reported an overspend on their high needs budget in 2016-17 totalling £139.5m.

The SEND crisis is also being felt in schools that are already grappling with an 8% real-terms reduction in funding since 2010, resulting in cuts to teaching assistants, specialist support and pastoral staff who play a vital role in supporting SEN pupils in mainstream settings.

In Kent, which is one of the biggest local authorities in England, high-needs spending rose from £119m five years ago to £167m this year. In the last 18 months there has been an 81% increase in requests for EHCP assessments. Part of the national increase in demand is due to the fact that the government’s SEND changes extended council liability to the age of 25.

Matt Dunkley, the director of children’s services in Kent, said: “I understand parents’ frustration on this – the 2014 legislation set out an expectation of what they are entitled to, but we have a system that is not currently funded sufficiently to meet their demands.

“It’s a crisis that threatens to undermine the general funding of schools, but also potentially to bankrupt local authorities who might have to bail out overspend from their own resources. We’ve got a perfect storm which is contriving to threaten the viability of the system.”

As mainstream schools struggle to support SEND pupils, a drift towards specialist schools – in particularly independent specialist schools – is an additional financial burden for councils. Official statistics show the number of children in private schools has risen from 3.7% of all SEND children in England to 6.9% in the last 10 years. Costs can be upwards of £50,000 a year per child; in a few extreme and complex cases it can cost £500,000 a year.

The House of Commons education select committee will meet this week to hear evidence as part of an inquiry into SEND. Robert Halfon, the Conservative MP who chairs the committee, said: “There are rising concerns about the quality and access to SEN provision, including the impact of funding issues and the very real difficulties parents face in securing help for their children.”

Councils around the country are consulting on proposals to cut SEND spending, while parents are crowdfunding to fight cuts in the courts. In August, families in Bristol forced the city council to reverse £5m of SEND cuts, parents in Surrey are awaiting judgment in a similar legal action to stop £22m of cuts, and parents in the London borough of Hackney are in the high court next week.

On the ground, parents say their children are losing home-to-school transport, speech therapy and one-to-one support as budget cuts bite. A petition signed by tens of thousands of parents calling for increased SEND funding is due to be handed to the education secretary, Damian Hinds, on Tuesday.

Families have also crowdfunded more than £10,000 to bring legal action against Hinds, as well as the chancellor, Philip Hammond. A “letter before claim” has been delivered accusing them of “failing to discharge their legal duties relating to the amount of funding allocated to SEND provision in England”.

Jo-Anne Sanders, the director of learning and early support at Kirklees, apologised for the council’s failings and said an additional £500,000 was being allocated to the SEND budget because of the pressure on resources.

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“The council has acknowledged the findings of the ombudsman and we also accept that we failed to make sure the child in question received the support they were entitled to for a significant period of time,” she said.

“The council has been working closely with parents, listening to their concerns and developing ways in which we can improve our services for children and families. We remain committed to making sure that all children are able to achieve the best possible start in life.”

The shadow education secretary, Angela Rayner, said: “The situation facing the UK’s most vulnerable children is so serious that the United Nations has warned that Britain is violating the international rights of disabled people, and thousands of disabled young people have been left without a school place at all.”

The minister for children and families, Nadhim Zahawi, said: “Core schools funding is increasing to £43.5bn by 2020 – this includes £6bn of funding specifically for children with special educational needs and disabilities, up from £5bn in 2013.

“But we recognise there are pressures on high-needs budgets due to increasing costs, which is why we have taken a number of steps to help schools and local authorities get the best value for every pound.”