Support for the online campaign surged as Leavers baulked at Brussels’ demands, including a sky-high Brexit divorce bill.
The petition, which calls for the UK to leave the EU right now, quickly soared past 100,000 signatures.
And that figure is the benchmark for a Commons debate on the issue.
Last week, it was revealed MPs will discuss it in Parliament on Monday, January 22.
The petition was set-up by Brexiteer Jack Taylor at a time when the UK’s negotiations with the EU were proceeding at a snail’s pace.
It demanded: “The Government should walk away from the Article 50 negotiations and leave the EU immediately with no deal.
“The EU looks set to offer us a punishment deal out of spite.
“Why wait another 18 months when we could leave right away and fully take back control of our country, lawmaking powers and borders?”
Mr Taylor said: “The EU looks set to offer us a punishment deal out of spite, insisting we pay tens of billions of pounds as part of a ‘settlement fee’ and continue to accept the jurisdiction of EU courts even after we’ve left.
“Meanwhile pro-EU MPs in Labour, the Lib Dems and the SNP, along with unelected Lords, are attempting to block Brexit, the longer we remain a member the more opportunity they have to interfere.
“Why wait almost another two years when we could just leave right away?”
Ukip, which has strongly supported the campaign, said the sheer level of support showed it was now time for politicians to listen to the people.
MEP and Ukip’s Brexit spokesman Gerard Batten said “Parliament will have to debate ditching Article 50 and leaving on our terms, not the EU’s.
“This is what should have happened the week after the Referendum. The genuine Leave MPs must now make a powerful case for immediate withdrawal.”
It is not known how many MPs will speak up in support of the petition, especially at a time when Mrs May appears to have gained support for her approach to the talks.
Her intervention last month saw EU leaders finally agree to move talks on to trade after offering £39billion to leave the bloc and satisfying them on EU citizens’ rights.
But the Government must wait until March to start trade talks, with no guarantee the final deal will be in the UK’s interests.
Even if it does, the UK is expected to be locked into a lengthy transitional arrangement.
Despite this week’s debate and the level of public support for the petition, it seems certain the UK will not abandon the Article 50 process.
The Department for Exiting the EU made clear a walkout was not on the cards, in its official response to the petition.
It said: “The Government has already introduced legislation to ensure the UK exits the EU with certainty, continuity and control.
“A smooth and orderly exit is in the national interest and further legislation will be introduced to deliver that.
“Both the UK and the EU should want to achieve the best possible outcome and the strongest possible partnership for the future. The Government believes that a deep and special partnership between an independent UK and the EU is in the interests of both sides.
“The country voted to leave the EU, and the Government is clear that there must be no attempts to remain inside the EU, no attempts to rejoin it through the back door, and no second referendum.
“In leaving the EU the Government will seek the best deal for the UK maximising the benefits from leaving the EU – control over our borders, laws and money – while maintaining the greatest possible access to EU markets and continuing to work with our European neighbours on common problems.
“After withdrawal, the UK will bring an end to the direct jurisdiction of the Court of Justice of the European Union (CJEU) in the United Kingdom.
“The Prime Minister has been clear that the days of Britain making vast contributions to the European Union every year will end.
“The European Commission has set out the European Union’s position on the financial settlement, and the Government is undertaking a rigorous examination of the detail of this.”