Two out of five staff at Lancashire Teaching Hospitals reported stress-related illnesses last year.
Healthcare experts say the figures indicate an "alarming downturn" in the well-being of healthcare workers.
The 2018 NHS Staff Survey revealed that 39 per cent of workers at the Lancashire Teaching Hospitals NHS Trust had felt unwell due to work-related stress over the past 12 months. That's higher than in 2017, when the figure was 36 per cent.
In addition, more than half the respondents admitted they had felt pressured into turning up at work during the last three months despite feeling too unwell to cope.
Unison's head of health Sara Gorton said government ministers were not paying enough attention to growing problems within the NHS. She added: "With so few staff, it's no wonder the pressures of working in the NHS are making so many health workers ill."
The survey, which received 3,613 responses from Lancashire Teaching Hospitals employees, also asked staff about their experience of working at the trust. The majority of staff were working overtime, with 68 per cent saying they worked extra unpaid hours on a weekly basis.
More than a quarter of respondents said they had been verbally abused or bullied by patients or members of the public, while 15 per cent had faced physical violence. The results also revealed that one in four staff had been verbally abused or bullied by fellow members of staff.
Professor John Appleby, chief economist at healthcare charity the Nuffield Trust, said: "After years of holding up against all the odds, these figures confirm an alarming downturn in the well-being of hard-working NHS staff. These pressures are not just a matter for staff themselves but have a knock-on effect on patients too."
Across England, four out of 10 NHS workers reported feeling unwell due to stress in 2018 - the highest level in five years. Neil Churchill, director of patient experience at NHS England, said: "Whilst there are a number of positives in this year's survey, it is also clear that local employers can do more to improve. We would expect all trusts to listen to the results from their staff survey and take appropriate action."