Data collected in the workplace suggests 420,000 employees in Britain in 2006 believed they were experiencing depression, anxiety or stress at work at levels that were making them ill.
One of the report's authors, Professor Cary Cooper, said a pressing issue was the number of workers who did not feel able to take time off when they were sick or stressed.
"Presenteeism" - where the individual is at work but not productive - could cost the UK around £900m a year.
Professor Cooper said employees in the UK already worked longer hours than in other European countries and that workers might feel under even more pressure to "put in the hours" given the unstable economic climate.
He said a work-life balance was essential for good mental health.
WAYS TO MENTAL WELLBEING
The Foresight report recommends five ways to ward off mental illness:
CONNECT: With people around you
BE ACTIVE: Exercise makes you feel good
TAKE NOTICE: Of your surroundings and savour the moment
KEEP LEARNING: Try something new or rediscover an old interest
GIVE: Do something nice for a friend or a stranger
He said new forms of flexible working could help employees meet these conflicting demands and still be financially viable and even beneficial for businesses by increasing workers' productivity.
He said: "We want more opportunities to request more flexible working arrangements. This is a business issue, it's not a soft issue. People who work flexibly can have more job satisfaction, be healthier and more productive."
Professor Cooper said companies could be required to make public their sickness absence rates and suggested performance indicators for managers.
The report also recommends occupational health experts are linked to primary care practices, which is usually the first port of call for people when they are feeling stressed or depressed.
The Foresight team also looked at what science could do to buffer against mental ill health, such as spotting and treating learning difficulties in children or developing biomarkers for dementia earlier in older people.
And they give practical ways that individuals can help to improve their mental wellbeing, such as keeping physically active and staying connected with friends and family.
Andy Bell of the Sainsbury Centre for Mental Health said stigma was another hurdle to overcome.
"Mental distress is a normal part of human life. One person in six experiences depression or anxiety in any year.
"The cost of ignoring mental distress at work is £1,000 for every employee in every UK business. A lot of this cost is hidden because of the fear and prejudice that still surround mental ill health.
Two years of work by over 450 experts
Looks at mental health and wellbeing from the cradle to the grave
Identifies threats and opportunities to improve the nation's mental health
The team will report back in 12 months on the project's progress, including action by other stakeholders
"Yet much of the cost can be saved by responding positively to mental distress at work and by taking simple, inexpensive measures such as allowing people to work flexibly when they are unwell and keeping in touch to offer help and encouragement when people are off sick."
The report, sponsored by the Department for Innovation, Universities and Skills, also calls for more training to ensure workers are able to compete in the global market for skills.
John Denham, Secretary of State for Innovation, Universities and Skills, said: "I welcome this report which provides new insights and creates fresh opportunities to offer support to individuals, families and organisations in building and sustaining mental capital and good mental health.
"My own department is investing more skills in training than ever before to ensure all of our people, young and old, can make the most of their talents and abilities, increasing their prosperity and improving their life chances while strengthening the wider economy."
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