A report by the Education Policy Institute (EPI) found that the number of referrals to specialist children's mental health services has risen by 26 per cent over the last five years.
Rejection rates were also found to be high and have not improved over the last five years, with 24.2 per cent of children referred for support being turned away.
The EPI estimates that at least 55,800 children were turned away for treatment in 2017/18 but the figure could be higher as a number of providers failed to disclose referral numbers to the think-tank's researchers.
The report, based on Freedom of Information Act responses from 54 child and adolescent mental health service (CAMHS) providers, and 111 councils, found that the main reason that referred children are being turned away is because their condition does not meet providers' threshold for support.
Analysis of threshold criteria from 41 providers found that young people who self-harm are only being accepted if they have another mental health condition such as depression or are suicidal.
Those with eating disorders are also being turned away because they are not between 10 and 15 per cent below their ideal weight. Such a criteria contravenes National Institute of Clinical Excellence guidelines that say this measure should not be used to determine treatment for such disorders, says the EPI report.
One provider was found to have "significantly increased" their threshold for treatment for anorexia between 2016 and 2017, the report also found.
"According to newly collected data, the number of referrals to specialist CAMHS has increased by 26 per cent over the last five years," states the report.
"By contrast, the population of young people aged 18 and under increased by three per cent over the same period - indicating that the rate of referrals has increased substantially."
It adds: "A conservative estimate of the number of rejected referrals in the latest year is 55,800, but the true number will be higher than this due to providers that did not respond.
"There is also wide variation between providers, with some rejecting approximately half of all referrals and some reporting that they rejected fewer than one per cent of young people referred this year."
In addition, the report found that since 2010 around a quarter of councils (27 out of 111) have axed early intervention services related to the mental health and wellbeing of children and young people.
Services being cut include community-based early help, support in schools, help for looked-after children and family support services.
The EPI is calling on the government to improve mental health support and reduce demand.
It wants to see the CAMHS workforce increased with their funding ringfenced and for services to have a focus on early help and school-based support for pupils with additional needs.
A child poverty reduction strategy also needs to be brought in to address the strong links between disadvantage and mental health problems.
"Our research finds no significant improvement in access to children's mental services over the last few years, with a number of treatment gaps evident in a system that is coming under increased pressure from rising referral rates," said report author and senior EPI researcher Whitney Crenna-Jennings.
"As many as one in every four children referred are denied access to specialist mental health services, often because their condition is not deemed serious enough to warrant treatment. Those excluded from treatment include children and young people that have self-harmed or experienced abuse.
"With a significant number of local authorities phasing out crucial services that offer alternative support, these children may find it increasingly difficult to access any formal help at all".
Last month research by drugs policy think-tank Volteface found that CAMHS are turning away young pepole with mental health issues linked to cannabis use, due to shrinking community health resources.
The government's December 2017 green paper, Transforming Children and Young People's Mental Health, pledged £300m in extra funding for children's mental health support. However, this is set to only cover between a fifth and a quarter of England and will not be launched until 2022/23.