The call for routine weekly tests for all health and care workers goes beyond the current NHS programme, which offers tests for staff who develop symptoms of coronavirus.
Labour has argued that rolling out routine weekly testing could help prevent transmission of the virus by health and care staff who are infected but remain asymptomatic - a problem one recent study called 'the Achilles' heel of current strategies to control COVID-19'.
NHS England said at the end of April that 'increased testing capacity means that we will now be able to extend the offer of regular testing to asymptomatic staff'. This has been adopted in some trusts, but not across the board.
Labour shadow health secretary Jonathan Ashworth said: 'Regular testing of all NHS staff must now be an urgent priority. Weekly testing of all healthcare workers reduces the spread of the virus and helps protect NHS staff and patients.
'Eventually resetting the NHS to continue treating COVID and non-COVID patients is going to have to take priority. This should include putting in place infection control measures to make sure patients can continue to safely receive their care, and routine testing of all staff should be a part of this.'
Doctors' leaders warned that any move to introduce regular testing would need to be backed by evidence and subject to regular review.
BMA public health medicine committee chair Dr Peter English said: 'Testing of healthcare staff - as in the wider community - can be useful in helping understand the spread of the disease and identifying new outbreaks.
'However, given what we know about the test’s accuracy, individuals should not place too much value in negative test results: for those self-isolating, a negative test is not a green light to go back to work. At the very least, individuals and members of their households need to be guided by their symptoms.
'Any proposal for an arbitrary interval for regular testing needs to be backed by evidence and this would need to be consistently reviewed as infection rates fall.'
One study found that one in five hospital patients infected with coronavirus may have picked it up in hospital, and that 89% of healthcare workers with COVID-19 had been infected in hospitals.
Further studies have also suggested that weekly testing of healthcare staff can reduce their contribution to coronavirus transmission by up to a third, and that a significant proportion of asymptomatic healthcare workers tested positive for COVID-19 during the peak of the outbreak.
A DHSC spokesperson said: 'The approach we are taking is repeat testing based on clinical need. Some people in hospital settings are at higher risk than others so it is better to focus resources on them. For instance, someone working in a finance department is at a much lower risk than someone in a frontline setting.'
The government has asked the Scientific Advisory Group for Emergencies (SAGE) for advice on routine testing and the appropriate frequency for rolling it out.