The UK government may have broken Parliamentary rules by not publishing Brexit legal advice, the Commons Speaker has said.
Mr Cox responded by insisting the Government has "gone out of its way" to satisfy Parliament's motion calling for the release of the full legal advice.
Once the results of the two votes were announced, Labour's Keir Starmer described the situation as "unprecedented" and noted that the legal advice must now be published in full.
May, for her part, has said the full extent of advice received by her government over the Brexit deal is confidential under lawyer-client privilege.
Labour demanded that it be done before next Tuesday when the vote on Mrs May's Brexit deal takes place.
The advice from a European Court of Justice advocate general emboldened supporters of EU membership in Britain's parliament on the first of five days of debate on May's plans to keep close economic ties after leaving in March.
The main thrust of Cox's advice is already known - the government released a 43-page document on it Monday in a bid to fend off the contempt motion. Never before has the House of Commons found ministers in contempt of parliament.
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It comes after one of the EU's top law officers, the advocate general Manuel Campos Sanchez-Bordona, stated on Tuesday his advice to the European Court of Justice (ECJ) that the United Kingdom could unilaterally stop Brexit by revoking Article 50.
The Government said after the vote that it would now publish the full advice. But defeat would increase the chances of a "no-deal" exit, which could mean chaos for Britain's economy and businesses, and put May under fierce pressure to resign.
The small Northern Irish party, the Democratic Unionists, which props up Ms May's minority Government, joined Opposition parties in voting against the Government on the contempt issue.
But he was also there not just to defend the prime minister, but to try and sell her deal to recalcitrant Conservative MPs by attempting to reassure them that her Brexit compromise - despite having "unattractive, unsatisfying elements" - was not going to trap the United Kingdom into a customs union with the EU forevermore.
Sky sources have been told that Mr Cox's legal advice concludes that the European Court of Justice would not in practice force the United Kingdom to stay in the backstop against its will if a case was brought by the government.
After the vote, the British pound fell to its lowest against the USA dollar since mid-August.