The union put the case for expansion to consultation group examining the laundry’s future.
The hospital is now considering two options for its Fulbourn laundry site - building a new NHS laundry, which could provide a better service, or closing the plant and handing the service over to a private contractor.
Martin Booth, chairman of the union’s Cambridge health branch, said: "We believe Unison has made a strong case for an NHS laundry for the future, and we strongly hope Addenbrooke's management opts for this.
"Our in-house service has a proven track record for quality, which we feel should be expanded and made available to a wider section of the public sector."
A spokeswoman for Addenbrooke's Hospital said: "The trust will be considering and evaluating the proposals put forward by staff and a decision will be made in April.
"The aim of this process is to ensure that an excellent laundry service is provided for the comfort and protection of our patients."
