The Local Government Association (LGA) said action needs to be taken because some children and young people are waiting up to 18 months for vital support.
As part of the Future in Mind initiative the government has set aside an extra £1.4bn for clinical commissioning groups (CCGs) for the period up to 2020 in order to improve child and adolescent mental health services (CAMHS), which they are responsible for commissioning.
A further £300m was announced in December to improve mental health support in schools and colleges.
The LGA said that around £90m - the equivalent of five per cent of the combined government commitment of £1.7bn - should be sufficient for every pupil in secondary and alternative education provision to have access to on-site school counselling services.
The figure is based on the assumption that over the course of a school year 10 per cent of the school population would be seen by a counselling service. Making provision for 50 counselling sessions per 100 pupils would equate to a total of around 2.25 million counselling sessions in England per school year.
With the cost of delivering a single session of school counselling estimated to be between £34 and £47 - extending provision to all state funded secondary schools and academies in England would cost between £76.5m and £105.8m per year.
The call forms part of the LGA's Bright Futures campaign for children and young people's mental health, which launched today. The LGA said evidence shows that on-site independent counselling services have led to a reduction in psychological stress in the pupils that have access to it, as well as improvement in behaviour and educational achievements.
Richard Watts, chair of the LGA's children and young people board, said: "No child or young adult should have to wait 18 months for vital support and guidance. Many young people might not have needed formal social care support if they had received the early help they needed.
"Providing just a small proportion of the funding it is spending on mental health support nationally to ensure every school provides on-site counselling is one way the government can ensure every child and young person enjoys the bright future they deserve.
"Mental health problems are very common and not something children should feel ashamed about. Good emotional health and wellbeing is also about learning to be resilient to life's setbacks and negative emotions.
"They may be facing personal problems outside of school that they feel that they are unable to talk to somebody about or in the current climate, it could be that they are seeking reassurance to cope with modern stresses such as social media pressures, sexual exploitation and negative body image."
A DfE spokeswoman said: "We recognise the value that school-based counselling can provide, and more than four out of five secondary schools offer access to counselling support for their pupils.
"To support schools, the government has pledged £1.7bn to help promote, protect and improve children and young people's mental health and wellbeing. Our proposals outlined in the children and young people's mental health green paper will provide significant additional resources for early mental health intervention.
"This includes improving the links between the NHS and schools, speeding up access to more intensive support, as well as boosting capacity to ensure early intervention."