But Dudley NHS Trust, which runs Russells Hall Hospital, and facility management company Mitie, has sought to reassure patients and staff members following the concerns highlighted by Unite.
Unite says it has identified a number of issues with the practices of Mitie, which is based within the hospital and is paid to look after the facility's upkeep.
Concerns raised include: social distancing is not happening; lack of ventilation; staff and visitors not signing in; failure to provide hand sanitizer; lack of security on site, monitoring visitors to its premises.
The premises of Mitie - which holds the facility management contract for the Dudley NHS Trust - is based in the hospital's estates department, which is away from patients.
Unite says that the concerns have resulted in the Health and Safety Executive (HSE) issuing a Notice of Contravention (NoC) - a document that sets out health and safety laws that have been broken - on Mitie, in relation to coronavirus safety.
But rather than close the facility, the HSE has given Mitie time to improve its Covid procedures, said a Unite spokesman.
Unite regional officer Su Lowe said: "This is one of the worst workplaces I have attended as a union officer since the beginning of the pandemic.
"Unite welcomes the intervention of the HSE, but this should never have been necessary, this is a large well-resourced company and strict Covid secure policies and practices should have been in place for well over a year."
In response, Mitie said it is working with the HSE on the issue.
A company spokesman said: "The safety and wellbeing of employees and patients at the NHS trust is our top priority.
"This includes maintaining a Covid-secure workplace for our colleagues as well as following government guidance regarding the use of hand sanitiser, PPE [personal protective equipment], social distancing and other measures. We are working closely with HSE in relation to this matter."
Diane Wake, chief executive of the NHS trust, said patients should still come to the hospital as normal.
She said: "As a trust we are committed to providing the safest, cleanest services for our patients, visitors and staff.
"We are proud that throughout COVID-19 we have protected our patients and staff and have some of the lowest rates of hospital transmission of Covid-19.
"The concerns reported relate to areas of Mitie’s non clinical offices which are in an area of the hospital, well away from any patient areas.
"We have strict infection prevention and control measures in place to keep our patients and staff safe and these apply equally to Mitie and all contractors moving around the hospital.
"It is very important that people who need to come to hospital do come to hospital. The public should be reassured that we are taking their health and safety very seriously."