Theresa May is to announce that all teachers in England and Wales will be trained to spot the early signs of mental health issues in children as part of a package of measures aimed at prioritising prevention.

With her premiership entering its final weeks, May is keen to salvage a domestic legacy from her three Brexit-dominated years in power.

She will visit a school in south-west London to highlight the importance of identifying mental health problems early, and make a series of promises, including the provision of new teaching materials to be used in classrooms and updated statutory guidance on schools’ responsibilities.

NHS staff will be encouraged to take suicide prevention training, and there will be updated professional guidance for social workers to oblige them to take relevant training.

“We should never accept a rise in mental health problems as inevitable,” May will say, calling failures in the treatment of mental illness one of the “burning injustices” she promised to fight when she arrived in Downing Street.

“It’s time to rethink how we tackle this issue, which is why I believe the next great revolution in mental health should be in prevention.”

The measures will be funded from a long-term increase in NHS spending announced by the prime minister last year: the government had already said spending on mental health would increase more rapidly than the overall health service budget.

May will also commit to overhauling the Mental Health Act, including by legislating against the the use of police cells to detain people experiencing a mental health crisis.

Sir Simon Wessely, who carried out a government-commissioned review of the act that was published last December, said: “The recommendations of the review of mental health legislation that she commissioned have been warmly welcomed from all sides but now need to be acted on. Today’s announcements are a further welcome step towards that goal.”

However, Labour said the package fell well short of the significant increase in funding for treatment that was necessary.

Barbara Keeley, the shadow minister for mental health, said: “The prime minister is failing to address the real crisis. Training for teachers and other professionals is welcome but when we know thousands of children and young people are either turned away from mental health services or have to wait too long for treatment, it’s clear that she’s missing the real issue.

“This Tory government has cut local authority funding and failed to protect mental health budgets. Labour will invest more in mental health services and ring-fence budgets so that funding reaches those who need support,” Keeley said.

Last week, May announced the government would legislate for a carbon emissions target of net zero by 2050, as she seeks to bind her successor into a series of modernising policies. She has also suggested that student maintenance grants should be restored.

But Philip Hammond has been keen to avoid signing off on any costly announcements, as the Treasury prepares for a spending review under a new prime minister – and almost certainly a new chancellor – in the autumn.

The news comes as the Children’s Society reports that as many as 106,000 10- to 17-year-olds a year with mental health problems are being denied care because specialist NHS services in England judge them to be not ill enough to need it. Only 79,000 of the 185,000 who seek help get it, the charity claims in a study.

The use of “thresholds” to decide which troubled children get treatment is unwise because young people who miss out are more likely to end up in crisis, it adds. Almost one in three (32%) of parents of children aged four to 17 say their child has been affected by a mental health issue in the last year, the charity found in a survey of 1,004 self-selecting parents.