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.
Britain's ministers have been forced to back down on Tuesday after parliament found the government was contempt over an order to publish full legal advice on prime minister Theresa May's Brexit deal with the EU.
Cabinet minister Andrea Leadsom announced the move after the Commons voted 311 votes to 293 to find ministers guilty of "contempt of parliament" for refusing to reveal the confidential advice.
The amendment gives MPs the power to instruct the government what action to take if May's Brexit deal is, as expected, voted down in Parliament.
Labour's shadow Brexit secretary Sir Keir Starmer said the finding of contempt was "a badge of shame" for the Government, with "huge constitutional and political significance".
He added: "I think there may be a whisper and a scintilla of an idea that somehow the Government wasn't deeply glooming about the fact that this might bully one or two into voting for the arrangement".
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.
May told parliament: "We need to deliver a Brexit that respects the decision of the British people".
As he presented his motion to the House, Mr Grieve said: "The House will recall that back in last June issues arose about how the House should proceed in the event of the Government's motion being rejected".
Theresa May is facing opposition in both directions over her Brexit deal.
"As MPs begin to debate Theresa May's bad deal, many will be reflecting on how it compares with the deal we've now got".
"And despite some of the bogus claims that have been made by those who oppose staying in the European Union, there would be no price to pay - political or financial - if we were to take back the Article 50 letter".
Ms Stihler said: "If judges accept his opinion, the United Kingdom will have the option of halting the process, and will be able to offer the chance to keep the best deal we have as a member of the European Union through a People's Vote - rather than choosing between Theresa May's bad deal or a catastrophic no-deal scenario".
Mrs May was due to open five days of parliamentary debate about her Brexit withdrawal deal ahead of a crunch vote billed for December 11.
May's government will now have to turn over the legal advice to Parliament.
May's spokesman, James Slack, said the opinion didn't change "the clear position of the government that Article 50 is not going to be revoked". "But I didn't play to gallery, I focused on getting a deal, that honours the referendum, sets us on course for a bright future and I did so through painstaking hard work".
Hardline Conservative Brexiteers say May's compromise deal does not represent enough of a break with Brussels.
The EU Withdrawal Agreement covers a settlement of £39 billion (US$49.8 billion) that Britain will have to play for leaving.