David Cameron has pledged an in-out referendum on Europe in 2017, and says he will not lead the country if he cannot guarantee to provide the vote.
The prime minister's comments, made on BBC One's The Andrew Marr Show, suggest he would not lead a minority government should the Conservatives fail to secure a parliamentary majority at the 2015 General Election.
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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.