About 360 contract cleaners at a hospital with one of England's worst rates of MRSA infection have voted to stage a one-day strike next month.
Some workers said they were "insulted" by the offer
The workers at Heartlands Hospital in Birmingham rejected a pay deal outlined by their employers, Initial Hospital Services, at a meeting on Thursday.
Unison said the deal amounted to an increase of 8p an hour, leaving members still 76p worse off than NHS staff.
The union has warned the action will "seriously effect" cleanliness.
Ray Salmon, West Midlands regional organiser for Unison, said: "Some (workers) were saying they were quite insulted.
"They've instructed me to go away and make preparations for industrial action.
"The strike is seriously going to affect the running of the hospital and cleanliness."
The cleaners and porters want the same hourly rate as their counterparts employed "in-house" by the NHS at Heartlands' sister hospital in Solihull.
Figures compiled by Unison show contract cleaners working at both hospitals currently earn £4.65 an hour, while porters take home £4.95.
Cleaners and porters employed directly by the trust earn £4.95 and £5.20 an hour respectively, with sick pay, pension provision and other benefits.
Initial Hospital Services said the new offer would give contract staff "pay parity" with their colleagues at Solihull Hospital.
A spokesperson said: "We urge our staff to accept this deal.
"Any industrial action would be disruptive for the hospital and it would cause unnecessary anxiety for patients."
But Unison said the new deal would see hourly pay for contract cleaners rise to only £4.93 and there was no offer for porters.
The union says NHS-employed staff are expected to reach an agreement to increase hourly their hourly rates to £5.69 an hour, backdated to 1 October.
"If we agree to this deal, the differentials on the hourly rate between NHS cleaners and contract cleaners will be 76p," said Mr Salmon.
He said a one-day stoppage involving about 360 union members was being planned for the first week in November.