"The House of Commons will today debate a motion finding Ministers in contempt for their failure to publish full legal advice concerning the EU Withdrawal Agreement", a deal reached between London and Brussels after months of hard negotiations, the parliament said on its website.
The government had previously published a summary of its legal advice, a move that was heavily criticized by MPs and led to the launch of contempt proceedings by six opposition parties.
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.
Never before has the full legal advice of any attorney general been published in its entirety.
Earlier, Shadow Brexit Secretary Sir Keir Starmer told MPs the government had been "wilfully refusing to comply" with the express will of parliament.
British Prime Minister Theresa May brushed aside questions Monday about whether she will resign if her Brexit deal is rejected by Parliament next week, saying she's confident she'll still have a job after the crucial vote.
And MPs backed a motion giving the Commons a direct say in what happens if her deal is rejected next Tuesday.
Commons Leader Andrea Leadsom said: 'We've tested the opinion of the House twice on this very serious subject.
British Prime Minister Theresa May is facing a full-blown constitutional crisis after the speaker's ruling.
Advocate General Manuel Campos Sanchez-Bordona told the European Court of Justice that EU law "allows the unilateral revocation of the notification of the intention to withdraw from the EU".
He said: "What I'm looking for particularly is what the legal advice says about our ability to strike any new trade deal".
Mrs May said Britain will leave regardless of any future decision by the EU's top court and that the choice is between her deal or no deal.
Chris Leslie, the Labour backbencher backing the amendment, said: "MPs are going to gradually assert their rights - including the right to instruct the government in future stages". Her former Brexit minister David Davis said: "This is not Brexit".
The British leader kickstarted five days of parliamentary debate on her proposed withdrawal agreement with a statement to parliament on Tuesday.
26 Conservative MPs ultimately voted for Grieve's amendment, further evidence on ongoing discontent in Tory ranks over Brexit.
May is battling to persuade lawmakers to support the divorce agreement she has sealed with the European Union when the House of Commons votes on December 11.
It means that instead of the government having to come back to tell MPs what their next steps are - and MPs voting on that - they would theoretically be able to vote on what they wanted the government to do as well. They claim that London will be forced to follow European Union rules without having a say in them; they also say that the European Union common external tariff will prevent London from enforcing free trade agreements on goods with non-EU countries.
Since most lawmakers oppose a no-deal Brexit, they could essentially take that option off the table.