The "scandalous" scale of the NHS's neglect of mental illness has been described in a report which suggests only a quarter of those who need treatment are getting it.

The report claims that millions of pounds are being wasted by not addressing the real cause of many people's health problems. Nearly half of all the ill-health suffered by people of working age has a psychological root and is profoundly disabling, says the report from a team of economists, psychologists, doctors and NHS managers, published by the London School of Economics.

Talking therapies such as cognitive behaviour therapy relieves anxiety and depression in 40% of those treated, says the Mental Heath Policy Group led by Lord Layard. But despite government funding to train more therapists, availability is patchy with some NHS commissioners not spending the money as intended, and services for children being cut in some areas. "It is a real scandal that we have 6 million people with depression or crippling anxiety conditions and 700,000 children with problem behaviours, anxiety or depression," says the report. "Yet three quarters of each group get no treatment."

Layard added: "Mental health is so central to the health of individuals and of society that it needs its own cabinet minister … The under-treatment of people suffering from mental illnesses is the most glaring case of health inequality in the NHS … Despite the existence of cost-effective treatments it receives only 13% of NHS expenditure. If local NHS commissioners want to improve their budgets, they should all be expanding their provision of psychological therapy."

A third of families have a member suffering a mental illness, the authors found. The report says mental health problems account for nearly half of absenteeism at work and a similar proportion of people on incapacity benefits.

In 2008, Layard and others won the argument that treating anxiety and depression saved the NHS money. A programme called Improving Access to Psychological Therapy (IAPT) was set up to train thousands more therapists.

Official figures, however, show that too few people are getting treatment across the country. There were 6.1 million with treatable anxiety or depression in England but only 131,000, or 2.1%, entered talking therapy in the last quarter of 2011.

There are stark differences between primary care trusts. Walsall did best, with 6.4% of depressed and anxious people in talking therapy, followed by Swindon with 5.8% and Northumberland with 5.5%.

But Hillingdon, west London had only 0.1% in treatment – 17 out of 29,000. Barnet and Enfield, both in north London, had 0.3% and 0.4% respectively.

Layard said commissioners were wrong "if they think 'why don't we cut a bit of that [talking therapies]' when they are spending money on infinitely lower priority conditions. Depression is 50% more disabling than conditions like angina, arthritis, asthma or diabetes." Even including those on medication, treatment only reaches a quarter of those in need.

Commissioners needed to understand that treating people with mental illness saves money, the report says. Layard pointed to a survey at two London hospitals which found that half the patients sent for an appointment with a consultant had physically inexplicable symptoms, such as chest and head pains for which there was no organic explanation. "These are people with somatic symptoms as a result of mental stress," he said.

In the long term he said he would like to see psychologists and therapists working alongside physical medicine doctors in the acute sector, to help determine the real cause of people's apparently inexplicable symptoms.

Dr Andrew McCulloch, chief executive of the Mental Health Foundation, said the report showed mental health remained a poor relation to physical health for the NHS. "The government has rightly committed to a parity of esteem between physical health and mental health in the health and social care bill, and surely they must now deliver on what they have promised."

Dr Clare Gerada, the chair of the Royal College of GPs, applauded the efforts of Layard and his colleagues to increase the availability of talking therapies.

"We live in a stressful society and the number of patients with mental health problems presenting to GPs is on an upward spiral," she said. "GPs face tremendous challenges in caring for patients with mental health problems in primary care and we welcome any development which will help us improve their care."

The care services minister, Paul Burstow, said: "Mental ill-health costs £105bn per year and I have always been clear that it should be treated as seriously as physical health problems … the coalition government is investing £400m to make sure talking therapies are available to people of all ages who need them. This investment is already delivering remarkable results."