Only four in 10 feel they have been trained well enough to help, although more than half of employees would go to bosses for help.
And 48 per cent of workers have at times felt too anxious or depressed to get up for work in the morning.
The survey, by employee engagement company Peakon, also found more women (58 per cent) said they had suffered these problems than men (42 per cent).
Dan Rogers, company co-founder, said mental health problems could strike at any stage. Until recently the topic had been taboo, especially at work.
He said: “The first step in offering support and providing staff with a healthy working life is to listen.
“It is vital employees have the ability to self-report any concerns, anonymously if required.
“It is only with accurate and honest feedback that companies are able to recognise and address the issues that are impacting employee well-being.”