The increasing support for the appeal comes after Boris Johnson asked the Queen on Wednesday to prorogue Parliament from mid-September until 14 October.
On Thursday morning around 1,000 people were signing it every minute.
Up until 28 August, it had gathered fewer than 100,000 signatures but numbers jumped following the row over the suspension of Parliament.
Mr Johnson spoke to the Queen on Wednesday morning to request an end to the current parliamentary session – a process known as prorogation.
The Queen approved the request at a meeting with the Privy Council – a group of senior politicians who advise the monarch – at her Balmoral estate on Wednesday.
According to an official statement, she consented to Parliament shutting down between 9 and 12 September until 14 October, when she will deliver the Queen’s Speech.
The Prime Minister insisted the decision was to allow his Government to bring forward new legislation but critics blasted the move as an attempt to hamper MPs’ efforts to block a no-deal Brexit.
A temporary suspension of a month gives MPs little time to implement legislation to avoid leaving the EU without a deal. They return to Parliament after summer recess on 3 September and Britain is due to exit the bloc on 31 October, regardless of whether or not a deal has been agreed upon.
On Wednesday, politicians against a no-deal Brexit were urging the public to add their support to the petition.
The Liberal Democrats’ Brexit spokesperson Tom Brake said: “Johnson’s plan to suspend Parliament is unprecedented, undemocratic and unacceptable. We must not let him shut down debate and stifle the voice of the people. Please sign this petition.”
Fellow Lib Dem MP Chuka Umunna, who defected from the recently-formed Independent Group for Change, tweeted: “You can show your opposition to Boris Johnson’s shameful undemocratic plans to prorogue Parliament by signing this petition.”
Labour MP Jo Stevens said: “If you’re outraged by the PM’s call to suspend democracy [please] sign.”
Any appeal on the official UK Government and Parliament Petitions website that secures 10,000 signatures is guaranteed a government response and 100,000 names sees the petitions committee consider it for debate by MPs.
This story first appeared on our sisted site the i.