In a shock intervention, Remainer Sam Gyimah said the Prime Minister’s future relies on her negotiating a favourable deal with Brussels.
And the frontbencher warned of a “terrible” prospect of hard-left Labour leader Jeremy Corbyn replacing her at Downing Street.
Speaking to Parliament’s magazine The House, he insisted Brexit would go ahead but warned the process would be “complicated”.
The Universities Minister said: “I voted Remain because I thought it was going to be costly and complicated extricating ourselves from the EU, not because I’m a big fan of Jean-Claude Juncker or anything.
“What the Prime Minister’s speech last week did well is that it reckoned with the difficult trade-offs that we have to make as a country.
“The truth is that we are leaving the EU, there’s no point in refighting the referendum battle.
“The important thing is thinking and looking ahead to what kind of regime and system we have post-Brexit to ensure that these sectors continue to be a success.
“But I guess ultimately we have a workable Brexit or Jeremy Corbyn ends up in Downing Street.
“And I think that would be a terrible thing for the country.”
Mr Gyimah’s comments will heap pressure on Mrs May at a time when relations between the UK and EU appear to be souring.
European Council president Donald Tusk yesterday accused the Prime Minister of trying to make Brexit a success “at any price”.
He also attacked her negotiating stance, warning Mrs May that a “pick and mix approach is out of the question”.
But the tough-talking bureaucrat insisted he wanted to strike “a trade agreement covering all sectors and with zero tariffs on goods”.