In 2015 a total of 1,090 of the 29,015 children assessed by councils (3.76 per cent) were denied an education, health and care (EHC) plan after being deemed not to require one.
Latest Department for Education figures, published today, show that the number of refusals in 2017 was 3,043 out of 45,205 assessments (6.73 per cent of the total).
EHC plans were introduced in the Children and Families Act 2014 and billed as providing children with special needs and disabilities more joined-up support from education, health and social care services.
The rise in refusals coincides with councils working to transfer thousands of children already on statements of special educational need on to new EHC plans in recent years ahead of the April 2018 deadline.
Earlier this month it emerged that all but 3,873 of the of the 236,225 children (1.6 per cent of the total) who had special educational needs statements when the transfer process began in September 2014 had been moved onto a new plan.
The figure represents a significant increase in the pace of children being moved from SEN statements to EHC plans over the past 12 months. In May 2017 the DfE reported that the number of children transferred to EHC plans had yet to pass the halfway mark.
But concerns have been raised that the scale of the task has placed pressure on local authority resources and some are not fulfilling their statutory obligations.
Children's services leaders have themselves warned that the system was not designed or funded to cope with the additional demand it is facing.
The DfE figures also show that the number of initial requests for support being refused, before they even reach the assessment stage, has increased in recent years.
A total of 8,870 initial requests for assessments for statements or EHC plans were refused in 2014, rising to 10,935 in 2015, and 14,795 in 2016. The figure for 2017 fell slightly to 14,568.
Children's minister Nadhim Zahawi said: "We want every child to have the support they need to unlock their potential, no matter what challenges they face.
"Thanks to this government's reforms, more children and young people with special educational needs and disabilities are getting the support they need at school and college, and the number who move on to access training schemes, apprenticeships or supported internships is increasing.
"But we are not complacent, and recognise there is more to do to make sure all children and young people have the right support to succeed in the future, and that families get help to navigate the new SEN system. That is why we are investing £25m to help schools deliver high-quality teaching, prioritise SEND support and create better links between mainstream and special education."
The education select committee is currently conducting an inquiry to review the success of the government's SEN reforms, how they have been implemented, and what impact they are having in meeting the challenges faced by children and young people.