The Prime Minister fears Jeremy Corbyn’s party wants to block a no deal Brexit by arranging a Commons vote using a rare parliamentary rule.
Senior Tories believe the move could force Mrs May to extend the Article 50 negotiating period in order to strike a deal with Brussels.
This would likely plunge the Government’s Brexit plans into turmoil by forcing the UK to stay inside the bloc beyond next March.
Downing Street recently warned Cabinet ministers that Mr Corbyn could use the ‘humble address’, an outdated Commons rule, to derail Brexit.
The mechanism – which has rarely been used in the past 200 years – allows MPs to vote on an issue without a bill being presented.
Labour has used the procedure twice in recent months to force Theresa May to release documents about Brexit.
One minister said: “We’ve been told by Number 10 that Labour would try to use the ‘humble address’ as a means to stop us leaving without a deal.”
Hilary Benn, chairman of the Commons Brexit committee, said a no-deal would be voted down by MPs regardless of which mechanism was used.
The Labour MP told the FT: “I think there is no majority in the House of Commons for a ‘no-deal’ Brexit and I think the Government knows that.”
Earlier this week, the Government was accused of stoking “apocalyptic” visions of a no-deal outcome.
Whitehall officials are reported to be making contingency plans to stockpile food and medicine if Britain leaves the EU without a deal.
But a Eurosceptic cabinet source said: “It is designed by No 10 to do the opposite of what Brexiteers want.
“We could have made a strong case for no deal and said we were prepared. The way they are presenting it makes it look like Armageddon.
“It is a kamikaze approach to no-deal. The truth is, it’s total chaos.
“They are deliberately trying to make no-deal look bad.
“It’s a fallacy to say it will be a total disaster. It won’t. We need to highlight the risk for the European Union, the negatives for them.”