Theresa May “will not countenance” revoking article 50 despite a public petition calling for the Brexit deadline to be cancelled adding almost 2m signatures in a couple of days.

When asked for the prime minister’s view on the petition, a No 10 spokeswoman said May worried that failing to deliver Brexit would cause “potentially irreparable damage to public trust”. She said: “The prime minister has long been clear that failing to deliver on the referendum result would be a failure of our democracy and something she couldn’t countenance.”

More than 2 million people had signed the plea for article 50 to be revoked by 11pm on Thursday. The list of names grew so rapidly that the parliamentary petition website crashed several times.

The petition began gaining significant support on Wednesday evening after Theresa May criticised MPs for not approving her Brexit deal. By Thursday, the list of signatures was growing so rapidly that the parliamentary petition website crashed several times. At the time of the first crash, the petition had received almost 600,000 signatures and was growing at a rate of 1,500 a minute.

At about 9am a message appeared stating that the site was “down for maintenance” and asking users to “please try again later”.

A House of Commons spokesperson told the Guardian: “The petitions site is experiencing technical difficulties and we are working to get it running again urgently. It has been caused by a large and sustained load on the system.”

The site was restored by 9.40am but collapsed several more times until it was fixed in the late morning.

Q&A What does the government do with online petitions? Show Hide After 10,000 signatures, petitions get a response from the government. After 100,000 signatures, petitions are considered for debate in parliament. Since the online petition service was launched, the government has responded to over 300 petitions, and 55 petitions have been debated in parliament. The government has already responded to a previous petition about revoking Article 50 on 19 February 2019, stating: 'The government’s policy is not to revoke Article 50. Instead, we continue to work with parliament to deliver a deal that ensures we leave the European Union, as planned, on March 29th'. This petition, which gained 148,912 signatures, was also debated in parliament on 11 March 2019.

By 3pm the petition had obtained its millionth signature. Ironically, the milestone was delayed as the weight of users checking for updates again forced the site briefly offline. By 11pm, it had gained 2m names.

The petition calls on the government to revoke article 50 and keep Britain in the EU. It states: “The government repeatedly claims exiting the EU is the will of the people. We need to put a stop to this claim by proving the strength of public support now for remaining in the EU. A people’s vote may not happen, so vote now.”

Tom Forth (@thomasforth) The best way to see where the "Revoke Article 50 and remain in the EU" petition is being signed is on the @ODILeeds hexmap viewer. A clear pattern, extremely concentrated in just a few places, and a very strong correlation with places that voted Remain. https://t.co/Fg9ZjycUdG pic.twitter.com/VdpcXHcKlw

The poll has been buoyed by support from celebrities including Hugh Grant, Jennifer Saunders and Brian Cox. The cause was also given surprise backing on Thursday morning by the chief minister of Gibraltar, Fabian Picardo, who told Sky News: “If on Tuesday MPs do not back the withdrawal agreement then the only way for the UK to take back control of the Brexit process is to revoke the article 50 notification.”

Tom Forth, the head of data at the Open Data Institute Leeds, said the distribution of signatures across the UK was uneven. The signatures were “extremely concentrated in just a few places, and a very strong correlation with places that voted remain,” he said.

Q&A What was the EU's agreement over extending article 50? Show Hide Special meeting of the European Council (Art. 50) (21 March 2019) – Conclusions 1. The European Council takes note of the letter of Prime Minister Theresa May of 20 March 2019. 2. In response, the European Council approves the Instrument relating to the Withdrawal Agreement and the Joint Statement supplementing the Political Declaration agreed between the European Commission and the government of the United Kingdom in Strasbourg on 11 March 2019. 3. The European Council agrees to an extension until 22 May 2019, provided the Withdrawal Agreement is approved by the House of Commons next week. If the Withdrawal Agreement is not approved by the House of Commons next week, the European Council agrees to an extension until 12 April 2019 and expects the United Kingdom to indicate a way forward before this date for consideration by the European Council. 4. The European Council reiterates that there can be no opening of the Withdrawal Agreement that was agreed between the Union and the United Kingdom in November 2018. Any unilateral commitment, statement or other act should be compatible with the letter and the spirit of the Withdrawal Agreement. 5. The European Council calls for work to be continued on preparedness and contingency at all levels for the consequences of the United Kingdom’s withdrawal, taking into account all possible outcomes. 6. The European Council will remain seized of the matter. Photograph: Eva Plevier/X06752

On Wednesday evening, Andrew White, the chief technology officer of the digital consultancy that built the petitions website, tweeted that the petition was receiving “an average of 1,000 signatures per minute. Not too bad, but nowhere near crashing the site – you all need to try harder tomorrow.”

The following morning, White conceded defeat and explained the technical error that had led to the failure. “Well done everyone – the site crashed because calculating the trending count became too much of a load on the database.”

This latest petition is not yet the biggest call for the government to put aside the result of the 2016 referendum. A petition launched before the referendum, calling on the government to run a second referendum if the vote for the winning side was less than 60% on a turnout of less than 75% got little attention before the vote but more than 4 million signatures afterwards.

The creator of that petition, William Oliver Healey, was a leave voter, who later expressed frustration that his petition had been “hijacked” by remainers. “This petition was created at a time (over a month ago) when it was looking unlikely that leave were going to win, with the intention of making it harder for remain to further shackle us to the EU,” he wrote on Facebook.