More than two-thirds of those who took part in the survey said they felt either stressed or under pressure at work.
And nearly three-quarters (73%) said their performance was affected by stress.
The results are based on the responses of more than 1,200 workers in full and part-time employment.
Workplace stress expert Professor Cary Cooper, of the University of Manchester Institute of Science and Technology (UMIST), said: "Until now, employers have associated stress with the occasional headache or day off work.
"However, they should be really concerned when three-quarters of workers say their performance is affected by stress."
Psychological claims
Unum's own figures show that the number of mental and psychological claims have risen by 88% over the past seven years. Those for chronic fatigue syndrome are up by 40%.
People who responded to the survey said that a shorter working day and a more understanding boss would do most to tackle the problem of stress.
Other potential solutions that were suggested included longer lunch breaks, and the offer of massage or reflexology sessions for staff.
Professor Cooper said: "The Unum survey confirms that a combination of long working hours and an autocratic management style are key sources of stress in the workplace.
"Employers need to move away from long working days as this does not result in increased efficiency - only increased levels of illness.
"Managers should become more oriented towards a greater praise and reward culture, and should also adopt more flexible working arrangements to help strike a better balance between home and work."