May denied collective Cabinet responsibility had broken down after three pro-EU ministers signalled that they could vote for the Cooper amendment.
Amber Rudd, Greg Clark and David Gauke said there was now a clear Commons majority in favour of extending the Article 50 withdrawal process rather than see a “disastrous” no-deal break.
The Prime Minister said it was “not a surprise to anybody” that there were strong views around the Cabinet table on the issue.
But with reports that up 100 Tory MPs could be prepared to defy the whips and back the amendment – with up to 20 ministerial resignations – May said a delay would not resolve the deadlock.
“Now, often people talk about the extension of Article 50 as if that will actually solve the issue. Of course it won’t. It defers the point of decision,” she said.
“There will always come a point where we have to decide whether we accept the deal that’s been negotiated or not. And that will be a decision for every member of Parliament across the House.”
Business leaders reacted with dismay to the latest Brexit delay.
Edwin Morgan, interim director general of the Institute of Directors, said: “There appears to be little realistic chance of a deal being agreed and the necessary legislation getting through by 29 March.
“Businesses do not want to drag out the uncertainty and would much prefer to reach a deal by the end of next month.
“However, it now seems hard to envisage an exit without a limited, technical extension to allow time for parliament to finalise our exit.”
He added: “Businesses have lost all faith in the political process and as those first in the firing line of no-deal, they deserve to know more.”
Josh Hardie, CBI deputy director general, said: “This is the latest signal to businesses that no-deal is hurtling closer. It must be averted.
“Every day without a deal means less investment and fewer jobs created.
“That’s the cost of running down the clock, and it’s irresponsible to treat that as a price worth paying.”