More than a third of workers are concerned about catching coronavirus on the job, according to a study by the Resolution Foundation think tank.
The poorest paid are particularly worried, the research found, but also the least likely to speak up about it.
Younger workers are also less likely to raise a complaint, the Resolution Foundation said.
The widespread concerns come despite government advice on making workplaces Covid-secure, researchers said.
Lindsay Judge, research director at the Resolution Foundation, said: "More than one-in-three workers are worried about catching coronavirus on the job, despite the extensive steps employers have taken to make workplaces Covid-secure.
"Given many workers' limited ability to get employers to address Covid concerns, the UK needs a strong enforcement regime to ensure that workplaces are as safe as can be.
"But instead health and safety resources have been cut, inspections have been slow, and Covid-related enforcement notices are few and far between."
The researchers said they were also concerned about the reduction in funding at the Health and Safety Executive.
The HSE's funding for each site it has the right to inspect has shrunk from £224 a decade ago to £100 for the current financial year, according to the report.
"The Foundation says policy makers should overturn the current view that health and safety is a 'brake on business' and take a more proactive approach to enforcement in the face of the pandemic," it said.
A government spokesman said £14m of funding was given to the HSE to combat coronavirus earlier this year.
An HSE spokesperson said: "We thank the Resolution Foundation for its report, and with our partners across government we will examine its findings. We welcome the acknowledgment of our increased activity and share the commitment to ensure all employees have a voice.
"Making sure Great Britain's workplaces are Covid-Secure is our priority; this effort will not be affected by recent additional restrictions announced across England, Scotland and Wales. We will work with stakeholders to deliver workplace health and safety during this coronavirus pandemic.
"Inspection and putting duty holders on the spot is just one part of a wide-ranging regulatory approach. We use a number of different ways to gather intelligence and reach out to businesses with a combination of site visits, phone calls and through a collection of supporting visual evidence such as photos and video footage."
While a new lockdown in England is planned from Thursday, up to half of the workers could still be going to work in jobs such as essential retail, education and health, Resolution said.
What are your thoughts and concerns about Covid?
Role of Businesses and Employers in Responding to COVID-19
Businesses and employers can prevent and [removed] . Employers should respond in a way that takes into account the level of disease transmission in their communities and revise their business response plans as needed. Employers should follow the [removed] , a phased approach based on current levels of transmission and healthcare capacity at the state or local level, as part of resuming business operations. Business operation decisions should be based on both the level of disease transmission in the community and your readiness to protect the safety and health of your employees and customers.
Businesses and employers are encouraged to coordinate with state external and local external health officials to obtain timely and accurate information to inform appropriate responses. Local conditions will influence the decisions that public health officials make regarding community-level strategies.
As an employer, if your business operations were interrupted, resuming normal or phased activities presents an opportunity to update your COVID-19 preparedness, response, and control plans. All employers should implement and update as necessary a plan that:
Talk with your employees about planned changes and seek their input. Additionally, collaborate with employees and unions to effectively communicate important COVID-19 information.
Plans should consider that employees may be able to [removed] even if they do not show symptoms.
All employers need to consider how best to decrease the spread of COVID-19 and lower the impact in your workplace. This should include activities to: