Nursing staff at the North Cumbria University Hospitals NHS Trust have passed a vote of no confidence in the board's management.
The Unison members were described as "down and demoralised" after a review which proposed a reduction in the number of nurses on the wards.
They said there was a risk this would affect patient care.
The trust said it was working with staff to meet the "significant challenges" it faced in the future.
All 1,100 Unison members at the Cumberland Infirmary in Carlisle and the West Cumberland Hospital in Whitehaven were balloted.
More than 620 papers were returned, and of those 98% said they had no confidence in the management, according to the union.
Christine Wharrier, the convener for Unison at the hospitals, said: "Staff are really down and demoralised.
"They feel that everything put in front of the trust board is nodded through, there doesn't seem to be any talking to staff, any explanation.
"The government has said that there should be a 30% cut in management costs, but what this trust seems to be doing is reducing it from the front line, and that will affect patient care."
Unison has sent the result to the trust board.
The trust said in a statement: "We note the result of this ballot from one of our partner unions.
"We are facing significant challenges in a very tough climate that is affecting many aspects of the public sector and the NHS.
"We therefore have to consider some difficult proposals and acknowledge that this will not be popular with everyone, but our aim is to continue to work closely with our staff and to involve them as we address these challenges."