Face coverings could soon be recommended in all public places in the United Kingdom including offices and other workplaces after ministers introduced laws forcing people to wear them in shops.
Officials have begun private talks with groups representing major employers amid growing fears over the prospect of a second wave of Covid-19 infections this northern autumn.
It came as a council in Lancashire became the first to order face coverings to be worn in all workplaces and enclosed public spaces following a rise in cases.
British Prime Minister Boris Johnson is expected to set out a fresh "road map" for his long-term strategy on Friday, when he will give details of how the country will get back to work without risking a second spike.
The new laws on face masks in shops were unveiled amid growing confusion over the Government's strategy, with even senior Cabinet ministers apparently at odds over masks.
Michael Gove bought food from a branch of Pret a Manger without covering his face, despite telling the public it was "good sense" and "good manners" to do so. However, Liz Truss, his Cabinet colleague, did wear a mask at the branch. The chain itself said it had no idea whether the rule would apply to it or not.
Johnson has faced a backlash from his MPs and ministers over the decision to force people to wear masks in shops, and a row broke out between retailers and Matt Hancock over a claim by the Health Secretary that deaths among shop staff had been "disproportionately" high.
Hancock told the House of Commons that Covid deaths among male sales and retail assistants were 75 per cent higher than the average, and 60 per cent for female staff, but Archie Norman, the Marks & Spencer chairman, said the claim was incorrect and "will make it less likely that people feel comfortable being in shops in the short-term".
There are growing fears that the move will deter already nervous shoppers from spending. Peter Cowgill, the J D Sports chief executive, told the BBC the introduction of mandatory face masks would negatively impact consumer confidence. He added: "I think it's the inconsistencies and the indecisiveness that causes the lack of confidence."
However, Hancock hinted at an extension to the rule, saying it was being introduced in "chunks".
George Eustice, the Environment Secretary, said: "When it comes to workplace environments, because people are in the same company throughout the day, there are not lots of people coming through the venue as you have in a retail environment; the risk of transmission is therefore lower."
But he refused to rule out telling people to cover their faces in offices and other workplaces.
Supporters of a blanket rule on face coverings in public places argue it is far easier to understand, and the Department for Business has contacted business representatives to canvass their views on more extensive use of masks.
The feedback from bosses was that they would support "any measures" that would increase consumer confidence, but asked for the scientific evidence backing such a move.
A government source said: "There are no current plans to recommend face coverings in all public places, but things are moving very quickly and nothing can be ruled out."
Hancock suggested that making face coverings mandatory in shops from July 24 was primarily for economic reasons, saying the British Retail Consortium had said they made shoppers "more confident about returning".
Blackburn with Darwen council said face coverings would be required in all workplaces and enclosed public spaces after a rise in cases. Residents would also be told to wear masks in libraries, museums, health centres and hair and beauty salons, it added.