The government last year pledged £1.4bn for child mental health by 2020, but a report says millions of pounds is being used to offset NHS cuts elsewhere.
Specialist teams are also turning away up to a quarter of youngsters, it said.
Health Secretary Jeremy Hunt said the government was "determined to address" mental health problems.
The previous coalition government promised in 2015 an extra £250m a year during this parliament to improve mental health services for children in England.
However, Liberal Democrat MP Norman Lamb - who was a health minister at the time - has now overseen a report by an independent commission that says much of the money has failed to reach the areas where it is most needed.
The report - by the Education Policy Institute Independent Commission on Children and Young People's Mental Health - says only £75m made it to the clinical commissioning groups who pay for services last year.
The commission says young people are still struggling to access help - partly because of difficulties in recruiting staff, including mental health nurses and psychiatrists.
According to the report, specialist services are turning away 23% of children and young people referred to them, often because there are "high thresholds" for accessing services.
The authors warned that "something has to go drastically wrong before some services will intervene".
The report challenged Theresa May to develop a "prime minister's challenge on children's mental health", similar to former PM David Cameron's "dementia challenge", which led to increases in investment and awareness.
Mr Lamb, chairman of the commission, said: "The prime minister, in her very first speech, rightly highlighted the inadequacies of the country's mental health provision as a 'burning injustice'.
"Today we call on the government to meet this commitment - and take urgent action to ensure children and young people with mental health problems receive the care they need."
Bev Humphrey, chairwoman of the Mental Health Network - which represents mental health and learning disability service providers in England - said the government had failed "to come close to fulfilling its existing promises on mental health funding".
"This situation means underfunded NHS and social services are struggling to help the growing number of children experiencing serious mental health problems.
"With many services almost at breaking point the commission is right - it really is time to deliver."
Mr Hunt said mental health services for children remained a priority and further plans to improve care would be announced "soon".
"We are already investing £1.4bn to help make sure children get the right care and every area in the country has put together plans on how they will spend the money to transform children's mental health services.
"We are also strengthening the links between schools and mental health services, and driving forward innovation to improve prevention and early support."
Money earmarked to boost mental health provision for children in England is failing to make it to front-line services, a new report suggests.