Children and teenagers are facing an “intolerable” mental health crisis and an urgent cash injection is needed in schools to prevent a lifetime of damage, teachers, doctors and MPs have warned.

Amid concerns about deeply worrying rates of self-harm and soaring numbers of children seeking help for problems such as eating disorders, teachers, campaigners and politicians have made a desperate plea to the government.

The intervention comes after a Children’s Society report revealed more than 100,000 children aged 14 in the UK are self-harming, with 22% of girls affected. The revelation was described as “deeply worrying” by the charity.

Teachers’ leaders have said schools are at a crunch point in terms of the mental health challenge facing classrooms, saying they feel overwhelmed and unable to cope. The warnings have been made as thousands of students head back to school after the summer holidays.

Sarah Hannafin, a senior policy adviser at the headteachers’ union NAHT, said: “There is a crisis and children are under increasing amount of pressure … Schools have a key role to play and we are doing what can, but we need more funding.”

Louise Regan, the former president of the National Education Union, added: “Teachers are overwhelmed by the sheer number of students showing signs of mental health problems … a primary teacher I spoke to recently said there was a child she felt really worried about. She was anxious about the pressure being put on her, but said she did not have anyone else to turn to for support.”

She said that counsellor and pastoral support staff numbers had been severely cut back, with money for children’s wellbeing desperately needed. “There is more focus on attainment measures rather than overall concern about the wellbeing of a child,” she said.

The mental health campaigner Natasha Devon echoed calls for funding. She said most schools no longer had money for a personal, social, health and economic education teacher, leaving a gap in learning about mental health and body image. She added that the government’s announcement in a new green paper of £300 million for mental health support in schools was just “plugging a hole”.

“My sense is the government keeps chucking little bits of money at the problem but what is needed is a significant investment, alongside a dramatic change in school culture,” she said.

The North Norfolk MP, Norman Lamb, said the UK faced an “intolerable crisis”; children only had one childhood and one education. “When it’s gone, it’s gone, and that will leave a lifetime of damage … We are failing an entire generation of young people.”

Last year, the government announced a £300m mental health plan for schools. This included incentivising every school and college in England to have a senior lead for mental health, creating new mental health support teams to liaise between schools and the NHS, and piloting a maximum four-week waiting time for children’s mental health services in some areas.

However, the initiatives will initially be piloted to assess their effectiveness, so the new forms of support envisaged will not be available across England until an unspecified time in the 2020s. The government’s ambition is only that they have been put in place in a fifth of the country by 2022-23.

Lamb said the plan was ambitious but the timescale was “hopelessly inadequate” and many children would not see its impact of it. He added that the latest figures on self-harm should be a “wakeup call” and that an urgent injection of cash was needed.

One teacher, working at a comprehensive school in Yorkshire, who asked to remain anonymous, said mental health was a growing and widespread problem. “One girl I teach scratches herself until she bleeds when she is stressed. Lots of students say they want to harm themselves … It’s usually because they have lots going on at home but also lots of things in school, for example, exam pressure,” she said.

She added: “I feel like a lot of what goes on in lessons is all about exam technique and preparing yourself, and not a lot goes into coping mechanisms … I am surprised more students have not fallen apart because of how stressful it is [in the exam years].”

Another teacher from a comprehensive school in Hertfordshire, also speaking anonymously, said: “We see more kids breaking down with anxiety, having to leave class. Some students in my class have panic attacks once a week and have to leave lessons.”

She added: “Sometimes you end up with 10 emails a day saying, ‘look out for this student and provide them with this’ … it can be overwhelming to spin all these plates and deliver good lessons.”

The soaring rate of mental health problems among young people, particularly girls, has been put down to a combination of social media, pressure from school, austerity and gender expectations. Calls were also made for a change in school culture and a switch of focus from exams to wellbeing.

Bernadka Dubicka, the chair of the faculty for child adolescent psychiatry at the Royal College of Psychiatrists, said social media created a new set of challenges for young people, but there were lots of other reasons young people became distressed. “Education is a big contributing factor … the system assessment is causing stress and strain for young people, but within the context of us living in an uncertain world and them having an uncertain future … They worry about unemployment, student fees and those who are not going to college to worry about how they are going to make a living and what the future holds for them.”

Laura, 20, who started self-harming when she was 12, said the prompt for her was family issues. “When it comes to girls and self-harm, it’s often assumed that the reasoning is because of looks and they’re being oversensitive but, in reality, there are many reasons why it happens.”

She added: “After a few months, my mum told my school about it and they were just about as unhelpful as my family. They kind of brushed it aside and offered me counselling, which I rejected due to not liking to talk about my problems, and then that was it.”

Laura said schools were not supposed to deal with such isses, but it would have been helpful if they had offered more support. “I feel like self-harm is still a taboo subject despite it being a major issue. Schools should take it more seriously … Parents need to be more educated, schools need to be more equipped to deal with it and teenagers need to stop joking about it.”

One mother, who asked to remain anonymous, said her daughter had been self-harming since she was 13, and lots of her friends did it too. “There are one or two of them in her friendship group but in terms of acquaintances I know of about 10.”

She added: “There are forums online where you can share scar photographs. There are support groups too but at the same time it is that weird thing of when does a support group become a window into what everyone else is doing.”

The mother said there was a lot more pressure on children now. “I could give loads of other examples of girls with eating disorders or other anxiety disorders. I know of about six children who have had to drop out of school completely and they are now in children’s mental health services. It seems out of control a bit.”

She said: “For the sake of children’s mental health, the education system needs to be urgently looked at. The pressure is huge now, with all the exam changes. It is just awful.”

• Children and young people in the UK who have concerns about mental health can contact Childline on 0800 1111. In the UK, Samaritans can be contacted on 116 123 or email jo@samaritans.org. In the US, the National Suicide Prevention Lifeline is 1-800-273-8255. In Australia, the crisis support service Lifeline is 13 11 14. Other international suicide helplines can be found at www.befrienders.org.