More than a quarter of English councils are acting unlawfully by discriminating against children with autism, according to a report by disability law experts.
Forty-one out of 149 local authorities have policies that denied families social care assessments, the Disability Law Service said.
Acting Lib Dem leader Sir Ed Davey, a patron of the service, said some cases were "discriminatory and unacceptable".
The Local Government Association said councils were "doing all they can".
Judith Blake, chair of the LGA's children and young people board, said: "Councils are under huge strain as a result of the rising demand for support - seeing an increase of 10% in education, health and care plans in the last 12 months alone."
Children with autism have the right to be treated the same as other disabled children under the Equality Act.
Local councils are legally required to assess disabled children to deliver the social care support they and their families would need - such as respite care and clubs.
The report found councils were blocking assessments and would only allow them if the child had an additional disability, showed a level of challenging behaviour or had been given an official diagnosis of autism.
Desperate for a break
Natalie Fawcett, from Scarborough, said she was desperate for a break from caring for her 14-year-old son Jordan, who has been diagnosed with autism, a moderate learning disability and severe anxiety.
"It's a constant battle to get the help and support," she said.
"We're absolutely not coping at all. Jordan doesn't sleep well and some nights I don't go to bed. Very recently I've been up for 50 hours."
Ms Fawcett said she had requested help over the past six years for Jordan to attend a suitable out-of-school club.
"I don't feel the support offered by the council is adequate or appropriate, I don't feel it's meeting my needs and it certainly isn't meeting Jordan's."
The report has not named the 41 councils, but the BBC knows the county council in North Yorkshire, where the Fawcett family lives, was one of them.
The council said its policies were neither unlawful nor discriminatory. Stuart Carlton, corporate director of children and young people's services, said: "We ensure families whose children have been diagnosed with autism receive a social care assessment if requested by the family, or another professional with the family's consent.
"These assessments identify any additional support we can provide, including respite.
"For those children who don't have a formal autism diagnosis and don't meet the criteria for the Disabled Children Service, we do all we can to support them in schools and other education settings".
Sir Ed Davey said the way some families of autistic children were being treated was "unlawful, discriminatory and unacceptable".
"These children have only one crack at childhood and if the law and the local authorities don't support them then those precious moments will be wasted," he said.
"It's vital those in charge of social care in every local authority step up to the plate, review their policies and make sure children are getting the social care needs assessments and support the law says they should."
The Liberal Democrat MP has written an open letter to councils highlighting "systemic and widespread discrimination against autistic children" and, without naming the councils, has urged them to put things right.
The government said it was increasing high-needs funding for local authorities by £780m this year and a further £730m in 2021-22, boosting the total budget for supporting those with the most complex needs to more than £8bn that year.
Prof Luke Clements from the University of Leeds' school of law, who led the research, concluded parents were being "let down and damaged".
His team analysed Freedom of Information responses and searched the council websites for their policies.
He warned some parents were being "humiliated by their local authority" and "treated very badly".
"I've been a lawyer for 40 years and I couldn't find some of these policies," he said.
"What a family with a disabled child with a myriad of other problems could possibly do I just don't know - they would have to give up."
The National Autistic Society said: "Families of autistic children up and down the country are being failed by the councils that are supposed to help them."
Head of policy and public affairs Tim Nicholls said the report was "damning evidence that far too many families have to fight too hard and wait far too long for the support their children need."
"What we hear too often is the families bumping along from crisis to crisis and, in the worst cases, children end up needing intensive support, end up in care or in mental health hospitals and that's exactly what we need to avoid."
How the BBC researched the story
The BBC launched its investigation in 2019 after families of autistic children and charities supporting them, namely the Disability Law Service and Cerebra, said there were serious problems in accessing assessments.
The Disability Law Service carried out some of its own research in 2017, which found some councils' policies to be unlawful. The BBC decided to contact every English council to find out if the discrimination was widespread.
Between April and September 2019 the BBC submitted Freedom of Information requests to all local authorities in England, requesting their policies for dealing with assessments of disabled children.
The University of Leeds joined the investigation towards the end of 2019 and provided a team of legal experts to analyse the policies and responses from the Freedom of Information requests.
They concluded 41 of the 149 English councils were breaking the law and discriminating against children with autism under the Equality Act 2010, meaning children with autism were not being given social care assessments and support for them and their families.
The joint report was due to be published earlier this year but was delayed because of coronavirus.