Mental health services for children and young people will fall well short of meeting a growing demand for help, despite pledges by ministers to increase funding, a report by Whitehall’s spending watchdog has found.

The National Audit Office said even if current plans to spend an extra £1.4bn on the sector were delivered, there would be “significant unmet need” because of staff shortages, poor data and a lack of spending controls on NHS clinical commissioning groups.

At present, one-quarter of young people who required mental health services were able to access help from the NHS, the report said. The Department of Health and Social Care hopes to increase the proportion to 35% – estimated to be equivalent to treating an additional 70,000 children and young people per year between 2015-16 and 2020-21.

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But the report, released on Tuesday, warned auditors had discovered “significant weaknesses and unreliability” in the government’s data, which undermined its plans. In particular, the NHS could not reliably track progress against one of its key targets to treat an additional 70,000 children and young people, they said.

Experience in other sectors suggests programmes to improve access to mental health services could uncover previously unidentified further demand, auditors said.

The report was released as Matt Hancock, the health and social care secretary, launched an initiative to put mental health on an equal footing to physical health across the world.

The Duke and Duchess of Cambridge, who have spearheaded the Heads Together initiative, joined ministers and delegates from more than 50 countries at an international summit in London.

Meg Hillier, the chair of the select committee on public accounts, said: “The government currently estimates that less than a third of children and young people with a diagnosable mental health condition are receiving treatment.

“But the government doesn’t understand how many children and young people are in need of treatment or how funding is being spent locally. The government urgently needs to set out how departments, and national and local bodies, are going to work together to achieve its long-term ambition.”

In December, the government published a green paper that pledged an additional £1.4bn over five years for young people’s mental health services and to increase staffing levels by 40%.

But the report said the government was still relying on data from a 2004 survey that found about 10% of five- to 16-year-olds had a mental health condition.

Slow progress on increasing the mental health workforce in England to 4,500 staff is emerging as a significant risk to delivering the government’s ambitions and there is no data available to monitor any increase, the report said.

In March, local areas planned to recruit only 3,410 NHS staff by 2020-21, auditors found. “This means that to meet the original ambitions, a quarter of new posts would need to come from outside the NHS, but local areas have not yet estimated how many non-NHS staff they will need,” the report said.

NHS England did not know whether additional funding for mental health services had been spent as intended by clinical commissioning groups, auditors found. “In reality, it has limited powers to ensure that CCGs increase spending in line with their intentions and it has chosen not to introduce any restrictions on how CCGs spend the additional funding received,” the report said.

An investigation by the Education Policy Institute released at the weekend found referrals to children’s mental health services in England had increased by 26% over the past five years, but nearly 25% of them were rejected, meaning at least 55,000 children were not accepted for treatment in 2017-18.

Most were rejected because their condition was not regarded as serious enough to meet eligibility criteria, including young people who had experienced abuse or showed evidence of self-harm.

Amyas Morse, the head 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 coordination.

“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.”