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Travellers could be fined or refused permission to board buses or trains if they refuse to comply with the order.
Face coverings can be a scarf, piece of cloth or mask.
Currently passengers are advised to wear a face covering but are not stopped from travelling without one.
At the Downing Street press conference on Thursday, Shapps said: “I can announce that as of Monday June 15 face coverings will become mandatory on public transport.
“That doesn’t mean surgical masks, which we must keep for clinical settings. It means the kind of face covering, you can easily make at home.”
Shapps said there will be exemptions to the rules for very young children, for disabled people and those with breathing difficulties.
He said on May 12 that 42 TfL workers and 10 mainline rail staff had died after being infected by coronavirus.
“We need to ensure every precaution is taken on buses, trains, aircraft, and on ferries,” Shapps said.
“With more people using transport the evidence suggests wearing face coverings offers some – albeit limited – protection against the spread for the virus.”
He added: “This will mean that you can be refused travel if you don’t comply and you could be fined.
“Alongside transport operators, this will be enforced by the British Transport Police if necessary, but I expect the vast majority of people won’t need to be forced into this, because wearing a face covering helps protect others.”
Sadiq Khan, the mayor of London, said he was pleased the “government has finally seen sense”.
“This is something I and others have been calling on ministers to do for some time, and is in line with a large body of evidence that they can help stop the spread of coronavirus,” he said.
Mick Cash, general secretary of the Rail, Maritime and Transport union, said the announcement was “long overdue”.
This article originally appeared on HuffPost.