The British Medical Association said there are more than 18,000 staff absent from acute hospital trusts in England.
The Government is facing calls to give NHS staff priority for lateral flow tests amid a shortage.
The Royal College of Nursing (RCN) and the British Medical Association (BMA) said health workers should come first when trying to access the rapid coronavirus tests in a bid to ease staffing issues.
The BMA said there are more than 18,000 staff absent from acute hospital trusts in England either with Covid-19 or because they are self-isolating, adding it expected that figure to be much higher when the most recent data is published later this week.
Dr Chaand Nagpaul BMA chair of council, said: “The Government has pledged that eight million lateral flow kits will be sent to pharmacies before New Year’s Eve.
“That’s a step in the right direction but there is no assurance that key workers will be offered them first.
“The BMA is urging the Government to do everything possible to ensure that enough tests are available for key workers as a priority.
“The rapid spread of the Omicron variant has no doubt had a massive impact on demand for lateral flow test kits and PCR tests, however it is vital that the promised new supply of kits are offered to key workers such as health and social care staff as a priority.
“Being unable to get the tests means staff may not be legally allowed to work, and at a time of acute workforce shortages and winter pressures this could be devastating for the care that can be given right across the NHS.”
Health Secretary Sajid Javid wrote to MPs over concerns about a dearth of lateral flow tests, saying the supply was being tripled in January and February from a pre-Omicron plan of 100 million to 300 million per month.
However, he said ministers expect a need to “constrain” supply for two weeks.
Pat Cullen, RCN general secretary and chief executive, said: “As the number of staff forced into sickness absence due to Covid-19 related reasons continues to increase it is vital staff have access to tests to protect themselves and their patients.
“We know, however, some staff continue to face problems accessing the tests online and would urge government to make the tests available for nursing staff as a priority, as well as ensuring there is the lab capacity for analysing tests.
“We also expect to see employers provide robust risk assessments for nursing staff caring for those with or suspected of having Covid-19. This included access to appropriate levels of PPE.”
Shadow health secretary Wes Streeting said he had written to Mr Javid urging him to make sure NHS staff were at “the front of the queue”.
He said: “Shortages of tests and delays in getting results risks exacerbating the staffing pressures in the NHS and other critical national infrastructure.”