The Government says the national minimum wage will increase by 12p an hour to £6.31 for adults and by 5p to £5.03 for 18-to-20-year-olds.
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Fellow designers including Tom Ford and Marc Jacobs have revealed they would refuse to do so.
Theresa May could face a Tory rebellion as MPs demand to see her plan for Brexit.
"I've never told anyone that before," she told the Today Show on a visit to a homeless shelter in New York.