One worker said: “I have been diagnosed with anxiety and depression but never admitted to it at work for fear of being stigmatised.”
Duncan Spencer of the IOSH said the findings were “deeply worrying”, adding that employers should create more open lines of communication.
A separate poll of 500 managers by business insurers QBE suggested that two out of five had lost contracts because employees continued to work despite having mental health problems.
Spokesman Grant Clemence said: “Businesses are beginning to recognise the beneficial impact that supporting mental wellness in the workplace can have.
“While some employers may see absence as a cost, not allowing employees to take time to recover when they need it could be just as damaging. Workplace cultures mean many are not taking time off when they need it.”
A poll of 2,000 adults by Mental Health First Aid England and Bauer Media found only one in 10 would feel comfortable speaking about issues such as eating disorders or postnatal depression.
Chief executive Simon Blake said: “Despite the increased awareness around mental health in the workplace, employees are telling us that there is still a significant gap in how we think and act about physical and mental health at work.”
Meanwhile, a survey of 2,000 workers by the conciliation service Acas showed two-thirds have felt stressed or anxious about work over the past year.
The most common reasons given for the way they felt included workloads, the way they were managed and balancing home and work lives.
Acas chief executive Susan Clews said: “According to our poll, the majority of workers have felt stressed or anxious about work over the past year.
“This is a cause for concern and it’s clear that active steps need to be taken to support the wellbeing of all staff.
“Our study found that seven out of 10 employees believe it is a line manager’s role to recognise and address stress or anxiety at work, but only two-fifths said that they would talk to their manager about it.
“It is clear that many people feel unable to have these conversations with their managers or choose to struggle alone.
“Acas has advice on how to create a positive mental health environment at work.”
Alan Jones is Press Association Industrial Correspondent.