The DfE should support teachers and schools by developing special educational needs and disability-specific guidance, claims the report, Special or Unique - Young People's Attitudes to Disability by disability programme Drill.
Among the recommendations is also a call for a minimum inclusion standard for disability awareness in the personal, social, health and economic (PSHE) education curriculum.
Ignorance of disability issues among schoolchildren, even those with special educational needs (SEN), is revealed in the report drawn from 11 focus groups with children aged 12 to 14, with and without special needs.
It found widespread frustration among pupils with SEN in both mainstream and special schools at the failure of teachers and school leaders to deal with bullying and to promote inclusive classroom environments.
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The report argues that supporting pupils with SEND to better understand their disability and the reasonable adjustments and support they can access, could improve academic outcomes and better prepare them for life with disability.
As well as uncovering widespread unhappiness with schools' response to bullying behaviour, the research suggests that young disabled people are often excluded from social networks and have few friends.
Drill is a five-year programme funded by The National Lottery Community Fund, aiming to build better evidence about approaches to disability and to inform future policy and service provision, as well as give a greater voice to disabled people in decisions that affect them.
Lead researcher Evan Odell from Disability Rights UK said: "These findings show that, in some areas, little has changed for disabled children in the last 40 years or so.
"Schools, special educational needs co-ordinators and teachers have understandably emphasised the need for reasonable adjustments and classroom support for pupils with SEND.
"Now they need to deal with bullying and ensure disabled children have the same chance to develop social skills and share in the experiences that mark out the teenage years."
The disability component of the PSHE curriculum, the report suggests, should be co-developed and co-delivered by disabled people's organisations working with schools and councils.
Kate Bowen-Viner, senior associate at education think-tank LKMco, which provided support with the design of the research, said: "We hope this research will help teachers, school leaders and policymakers better understand how they can support young disabled people.
"The research also highlights the value of creating forums for young people to reflect critically on the perceptions they have of their peers with special educational needs and disabilities."
The report also recommends that school leaders should foster greater openness about SEND and disability in the school, and support pupils with SEND to understand their own disability.
Local disabled people's organisations should also be involved in planning and delivering PSHE lessons on disability, it says.
In 2017, a United Nations report criticised the treatment of disabled children in the UK, and called on the government to provide better support.
The DfE said that between September 2016 and March 2020 it was providing £2.8m of funding to anti-bullying organisations to support schools, including the Anti-Bullying Alliance which has a particular focus on SEND.
It added: "Schools should be safe places where children are taught to respect each other and staff.
"Any kind of bullying and harassment in schools is completely unacceptable.
"We are making Relationships, Sex and Health Education compulsory from September 2020.
"The new guidance states that that these subjects must be accessible to all pupils and is particularly important when planning teaching for pupils with SEND, encouraging pupils to treat all their peers equally."