Jessica Best, a housekeeper at Dorset County Hospital, said the move would be bad for staff at a time when morale was already “very low”.
“We’re very proud to work for the NHS,” she said, adding: “It feels like that’s being taken away.”
Frank Goodwin, a security officer at the hospital, agreed.
“It’s making me feel like we’re second class citizens,” said the 39-year-old.
“You’d never take the nurses or the doctors out and try to fund them separately, and find a way to make them not part of the NHS.
“I’m part of the NHS because I care, I want to work in a sector where I’m bringing something to society. I don’t want to be just some contractor.”
Ms Best said there were also fears over what it would mean for their contracts.
“We’re very concerned about our terms and conditions,” said the 47-year-old.