The figures, based on a survey of almost 1,500 primary headteachers, were released by children's charity Place2Be and the National Association of Head Teachers (NAHT) as part of Children's Mental Health Week.
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Findings further show that even in school's with the dedicated counsellor, in most cases, the mental health professionals are on site for just one day or less a week. There are around 4.5 million primary state school pupils in the UK, meaning there are as many as 3 million pupils who are not getting access to adequate support.
According to the research, nearly four in five schools (78%) cite financial constraints as a barrier to providing their pupils with adequate mental health services. More than half (53%) blame a shortage of services or qualified professionals.
One headteacher, who did not wish to be named, said: "If we could access specialist support early for our children I think some of the issues seen later in their education could be avoided."
Catherine Roche, CEO of Place2Be said primary school leaders are well aware of the challenges their pupils faced, "whether it's coping with parental separation, the illness or death of a loved one, or even witnessing domestic violence or substance misuse at home.
"The vast majority are already working hard to support them so that they're ready to learn and can get the most out of their education,” she said. "But teachers are not counsellors and sometimes schools need professional support to make sure that problems in childhood don't spiral into bigger mental health issues later in life."
The charity's second annual Children's Mental Health Week has the theme of 'building the resilience of children and their ability to cope with stressful situations'. Ms Roche adds that she hoped to encourage school staff to "focus on understanding a child's behaviour and helping them to manage their emotions in a positive way".
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