The 3 Dads Walking say they are disappointed the government has not committed to making suicide prevention part of the national curriculum.
Mike Palmer, from Greater Manchester, Andy Airey from Cumbria and Tim Owen, from Norfolk, known as 3 Dads Walking, took on their latest challenge to walk to the Parliaments of the UK in a 600-mile walk to raise funds for suicide prevention charity Papyrus.
The trio, who have raised awareness of mental health and millions for charity also collected more than 100,000 signatures on a petition supporting the plan.
But despite the huge backing, including from many MPs, the government says it will only commit to a review of the curriculum.
In response to the government's statement, the 3 Dads said, "quite frankly it's not good enough".
Mike Palmer, from Sale, voiced his disappointment, saying: "It's a logical thing to do.
"You start early years, you teach young kids about their emotions, and it's ok to be happy, sad and angry.
"You teach them how to reach out, you build on this through primary school, into secondary school, into higher education, universities. You build on it.
"These life skills surely as important as a lot of the academic qualifications."
The dad's walk began in Belfast in September, where they walked to the Northern Ireland assembly at Stormont.
They then took a flight to Edinburgh, where they continued their walk from the Scottish parliament at Holyrood.
From there they walked down the country, through the North West to the Welsh Assembly at the Senedd, before walking across to Westminster in London.
It was the dad's second walking challenge, after the trio raised almost £1 million in 2021 walking between their three homes.
In a statement the Government said: "All pupils in schools are taught about mental health as part of the Relationships, Sex and Health Education (RSHE) curriculum, which we made mandatory in 2020 to ensure that all pupils are taught about important topics.
"Through health education, pupils learn to recognise the warning signs of poor mental health, in themselves and in others, which could lead to self-harm or suicidal thoughts.
"This includes learning about the common types of mental illness, such as anxiety and depression, understanding that experiencing poor mental health is not uncommon and knowing where and how to seek support for themselves or someone else, whose mental wellbeing they are worried about.
"Schools can teach older pupils about suicide in an age-appropriate and sensitive way.
"The RSHE statutory guidance advises that schools should approach teaching about self-harm and suicide carefully and should be aware of the risks to pupils from exposure to materials that are instructive rather than preventative, including websites or videos that provide instructions or methods of self-harm or suicide."
The government department added: "The guidance is clear that where teachers have concerns about a specific pupil in relation to self-harm or suicidal thoughts, they must follow safeguarding procedures immediately.
"The Department for Education (DfE) is committed to review the RSHE statutory guidance, which we plan to start in 2023.
"As part of the review process, the DfE will undertake a public consultation on proposed changes to the current guidance.
"Respondents will be able to comment on the proposed changes and to propose additional changes for consideration
"We expect to complete the review process and publish the updated guidance in 2024.
"We are also offering a grant of £1,200 for eligible state-funded schools and colleges in England to train a senior mental health lead to develop and implement a whole school or college approach to mental health and wellbeing.
"Senior mental health leads can support staff training so that schools cover issues that their pupils need to know about in a safe way.
"The DfE continues to work closely with the Department for Health and Social Care (DHSC) around issues of children and young people’s mental health and how to provide support to pupils as early as possible."
Worried about mental health?
It also supports those bereaved by suicide, through the Support After Suicide Partnership (SASP).
Phone their helpline: 0800 585858 (Daily, 5pm to midnight)
Mind is a mental health charity which promotes the views and needs of people with mental health issues.
Phone Infoline on 0300 123 3393
Suicide is the biggest killer of young people in the UK. PAPYRUS aims to reduce the number of young people who take their own lives by breaking down the stigma around suicide and equipping people with the skills to recognise and respond to suicidal behaviour.
HOPELINEUK is the charity’s confidential helpline service providing practical advice and support to young people with thoughts of suicide and anyone concerned about a young person who may have thoughts of suicide.
HOPELINEUK is staffed by trained professionals, offering a telephone, text and email service.
YoungMinds is a resource with information on child and adolescent mental health, but also offers services for parents and professionals.
It is the UK’s leading charity fighting for children and young people's mental health, and wants to make sure all young people can get the mental health support they need, when they need it
YoungMinds Textline - Text YM to 85258
Phone Parents' helpline 0808 802 5544 (Monday to Friday, 9.30am - 4pm)