Telling everyone to wear face masks in public could put the supply to frontline staff at risk, hospital leaders have said.
Wearing masks is compulsory on public transport and in shops in Austria, Czech Republic, Slovakia and New York.
And the London mayor Sadiq Kahn has said the capital should follow suit.
The government is carrying out a review into the usefulness of masks in preventing the spread of infection, despite the World Health Organisation (WHO) saying there is no evidence to support their use by the general population.
And Chris Hopson, chief executive of NHS Providers, has asked the government to make sure the impact on hospitals of any change in advice is fully assessed.
In a statement he said: Fluid repellent masks for health and care staff are key to safety and to avoid the spread of coronavirus.
Securing the supply of masks, when there is huge global demand, is crucial. This must be a key consideration for Government.
There needs to be clear evidence that wearing masks, along with other measures, will deliver significant enough benefits to take us out of lockdown to potentially jeopardise NHS mask supply.
The government has faced repeated questioning over the quality and supply of masks and other Personal Protective Equipment (PPE) to frontline medical staff and care workers.
Last week the Health Secretary Matt Hancock said he and his colleagues won’t rest until all health and care workers have got adequate supplies of kit like masks, gloves and aprons.
The Royal College of Anaesthetists has become the latest medical union to suggest its members should not treat patients without proper equipment.
WHO guidance issued earlier this month acknowledged that the virus could be passed on by people who are not yet symptomatic, but it said: Current evidence suggests that most disease is transmitted by symptomatic, laboratory confirmed cases.
There is currently no evidence that wearing a mask (whether medical or other types) by healthy persons in the wider community setting, including universal community masking, can prevent them from infection with respiratory viruses.
It warned that the use of masks by the public can create a false sense of security and lead to people ignoring other protective measures, such as hand hygiene and physical distancing.
Masks can even be a source of infection when not used correctly, the WHO added.