Tory MPs Peter Bone and Philip Hollobone backed the contempt motion, along with nine MPs from the DUP - who are supposed to be Mrs May's parliamentary allies. The government immediately pledged to publish the legal advice, prepared by Attorney General Geoffrey Cox, on Wednesday.
Ministers are expected to set out tomorrow how this will be done.
The debates and final vote on December 11 will determine how, and possibly even if, Britain leaves the European Union as planned on March 29, in the country's biggest shift in foreign and trade policy in more than 40 years.
With the prime minister's challenge in winning next week's vote looking all but insurmountable, MPs in the deeply-divided House of Commons are increasingly concerned about what happens next.
But the debate was delayed as MPs voted on the contempt motion.
Following Tuesday's vote, the privileges committee will decide which ministers should be held accountable for this failure and what sanction to apply, with options ranging from a reprimand to a potential suspension from the House of Commons.
The government is facing a vote today over whether it is in contempt of Parliament by refusing to publish its own Brexit legal advice. "The Prime Minister can't keep pushing parliament away or avoiding responsible scrutiny".
He added: "Theresa May's majority has evaporated, and the credibility of her deal is evaporating with it".
British lawmakers held up a momentous Brexit debate on Tuesday (Dec 4), accusing the government of contempt over its handling of the withdrawal agreement, as a top European Union legal opinion stated Britain could even call off its departure from the bloc altogether.
Leadsom said: "We've tested the opinion of the House twice on this very serious subject.
Don't imagine that if we vote this down another deal is going to miraculously appear", Mrs May insisted.
"This is the deal that will ensure that happening in an orderly way, with legal certainty".
"That possibility continues to exist until the withdrawal agreement is formally concluded", he said.
"The British people want us to get on with a deal that honours the referendum and allows us to come together again as a country, whichever way we voted", she will tell lawmakers on Tuesday, according to excerpts of her speech.
Sterling then recovered after an amendment on handing Parliament a greater say, should the Brexit deal be defeated on 11 December, was approved.
- The BBC dropped proposals for a TV debate featuring Mrs May, Labour leader Jeremy Corbyn followed by a discussion between eight panellists including politicians from different sides of the Brexit argument.
The court's advocate general said that Article 50 "allows the unilateral revocation of the notification of the intention to withdraw from the European Union".
The guidance is not binding on the Luxembourg court, which is considering the issue in response to a request from British parliamentarians.