The government had attempted to have the issue referred to the cross-party Privileges Committee in a prior vote but the proposal was defeated by four votes.
Some 26 Tory MPs - including former ministers Sir Michael Fallon, Damian Green and Sir Oliver Letwin - rebelled on the amendment tabled by ex-attorney general Dominic Grieve.
The U.K. voted 52 percent in favor of leaving the E.U. on June 23, 2016, after joining the bloc in 1975, when it was a collection of markets and industries under a common European grouping.
Senior government ministers are facing possible suspension from the House of Commons days before a crucial vote on Brexit after they were accused of holding Parliament in contempt. It is highly regrettable that the government has let it come to this, but ministers left the opposition with no option but to bring forward these proceedings.
"Never before has the House of Commons found ministers in contempt of parliament".
May refused to publish on the basis that such "candid" legal advice given to ministers should be understood to be confidential.
It came after Attorney General Geoffrey Cox published a summary of the advice on Monday and answered MPs questions for three hours - but said that full publication would not be in the national interest. See PA story POLITICS Brexit.
Mrs May's appearance in the Commons on Tuesday will coincide with a presentation at the European Court of Justice, which is hearing a claim by a cross-party group of Scottish MPs, MSPs and MEPs that Westminster politicians could reverse Article 50 - the clause that initiated Brexit - without the consent of the 27 other EU member states.
But May's spokesman told reporters: "It does nothing in any event to change the clear position of the government that Article 50 is not going to be revoked".
Meanwhile, Mr Carney stepped up his warnings about the potential impact of a no-deal Brexit.
He told the Commons: "That is contempt".
"I never said this deal was ideal, it was never going to be".
Reflecting on her personal journey, May added: "I have spent almost two years negotiating this deal".
For starters, there has been little agreement in parliament on much of anything except that no one likes the deal May secured.
"What we break now may be very hard to fix later", Leadsom said.
The decision is expected to be made by the end of the year, but judges at the ECJ must first accept jurisdiction over the case.
"I'm focusing on ... getting that vote and getting the vote over the line", she said.