More than 600,000 people have now signed the petition, which calls for support to remain in the EU, surpassing the 100,000-signature threshold needed for it to be debated in Parliament.
There was increased activity in signatures following the Prime Minister's appeal to the public on Wednesday night.
In her Downing Street statement, she blamed MPs for failing to implement the result of the 2016 EU referendum and told frustrated voters: ‘I am on your side.’
Revoke Article 50 began trending on Twitter following Mrs May's speech and continued to be a global trend into Thursday morning.
Users were quick to share the petition, with celebrities and MPs tweeting their support for Parliament to revoke the Treaty of Lisbon clause which deals with leaving the EU.
Famous figures including actors Hugh Grant and Jennifer Saunders, TV presenter and author Caitlin Moran, physicist Brian Cox and former Labour press chief Alastair Campbell all urged their followers on social media to sign the petition.
Alongside the link, Grant wrote: ‘I've signed. And it looks like every sane person in the country is signing too. National emergency.’
The petition had reached more than 610,000 signatures before the website began showing an error message shortly after 9am on Thursday, with around 584,000 of those signing from the UK.
The error was later rectified and the number of signatures began increasing once again.
The petition reads: ‘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.’