The health secretary, Jeremy Hunt, has said there should be a second referendum - or another general election - to vote on the terms under which the UK will leave the EU.
In an article for The Telegraph, Hunt explains why he believes the referendum was lost, calls on the UK to stay in the single market and explains why there needs to be a new vote on the UK's role in Europe.
"We did not vote on the terms of our departure," Hunt said.
"Before setting the clock ticking, we need to negotiate a deal and put it to the British people, either in a referendum or through the Conservative manifesto at a fresh election.
"The knowledge that once again we will trust the British people to decide on whether or not it is a good deal will concentrate minds across the Channel."
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If Hunt does want to run for the leadership, he will need to make his intentions clear fairly soon. Nominations to be on the ballot open at lunchtime tomorrow and will close on Thursday evening. George Osborne this morning took himself out of the running, while Theresa May was found to be the most popular choice among Conservative votes - ahead of second-placed Boris Johnson.