A report by the NAO highlighted "significant weaknesses and unreliability" in government data on numbers of children affected by mental health problems.
The government wants to increase the proportion of children and young people in need of support who are able to access NHS-funded mental health services from around 25 per cent to 35 per cent - estimated to be equivalent to treating an additional 70,000 children and young people a year - between 2015/16 and 2020/21.
However, the NAO said government cannot "reliably report progress" directly against the 70,000 target, as it does not have a reliable baseline measure.
The report says the spending watchdog has further concerns about the equivalence of the 70,000 target to the desired 10 per cent increase in access rates.
"It does not yet have consistent and reliable data available on the number and proportion of young people accessing treatment each year, so NHS England cannot be confident about the growth rates in access," the report states.
The report goes on to say that if current initiatives are delivered as intended, there would remain significant unmet need for mental health services among young people, with experience in other sectors suggesting that programmes to improve access to mental health services may also uncover previously unidentified further demand.
Concerns are also raised that not all of an additional £1.4bn of extra funding, through the Future in Mind initiative to improve children and young people's mental health services between 2016/17 and 2020/21, is reaching the frontline.
The NAO said NHS England cannot be sure the money is being spent by clinical commissioning groups on young people's mental health. NHS England also has only limited powers to ensure the money is reaching its intended destination, adds the report.
Figures published in parliament last month revealed that more than a quarter of money already made available through Future in Mind is not going to frontline services.
Further concerns are raised by the NAO that the government has not made enough progress to increase the mental health workforce.
The government has set a target of boosting the workforce by 40 per cent (4,500 staff). But just 3,410 extra roles are being planned for, according to local data released in March this year.
"The government has laudable ambitions to improve mental health services for children and young people," the report states.
"It started from a very low base when it developed its strategy and has prioritised improvement programmes which take an important, if modest step towards achieving its aspirations.
"The government has not yet set out or costed what it must do to realise these aspirations in full and there remains limited visibility of activity and spending outside the health sector.
"While the NHS has worked to improve information on its activity and spending, significant data weaknesses are hampering its understanding of progress. Slow progress on workforce expansion to deliver NHS services is also emerging as a major risk to delivery."
Amyas Morse, comptroller and auditor general of the NAO, said: "Parity of esteem between physical and mental health services for children and young people is a laudable aim. However, to deliver meaningful change, this must be matched by the necessary planning, resourcing and co-ordination.
"Despite a welcome start this aim remains far off. Current targets to improve care are modest and even if met would still mean two-thirds of those who need help are not seen.
"Rising estimates of demand may indicate that the government is even further away than it thought."
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, particularly within schools. But this is set to only cover between a fifth and a quarter of England and will not be launched until 2022/23.
Action for Children policy and campaigns director Imran Hussain has described the NAO's report as revealing a "disappointing picture" of government progress on children's mental health.
"It's clear the government is failing to grasp the scale of the crisis," he said.
"The only way to halt the growing threat to children's mental health is to ensure preventative help services are put in place now, not in four years' time."
Young Minds policy director Dr Marc Bush said the NAO report should act as a "wake-up call" for the government.
"After decades of underfunding, there have been welcome improvements in children and young people's mental health services - but the reality is that they remain overstretched and inconsistent," he said.
"Every day we hear from parents who simply can't get the help they need for their children, or from young people who have become more ill during the wait for treatment.
"With demand rising, we urgently need to see increased funding for specialist mental health services, alongside improved accountability to ensure that all the money is spent where it's intended. We also need action to recruit and retain staff, and to ensure that there is better support in the community when problems first emerge."
Earlier this month a report by the Education Policy Institute revealed that as many as one in four young people referred to specialist children's mental health services are being turned away. This comes as providers struggle to cope with rising demand, with referrals increasing by 26 per cent over the last five years.
The Department of Health and Social Care spokesman said: "Our ambitious plans to transform mental health services for children and young people are supported by £1.4bn and put us on track to ensure 70,000 more children a year have access to specialist mental health care by 2020/21, as well as improving access to services through schools with a brand new dedicated workforce.
"We are completely committed to achieving parity between physical and mental health as part of our long-term plan for the NHS, backed by an additional £20.5bn of funding per year by 2023/24."