The list of names grew so rapidly on Thursday the official parliamentary petition website crashed several times.
A House of Commons spokesperson said the site had experienced technical difficulties but added staff were working to get it working again urgently.
The numbers signing swelled as fears of a No Deal Brexit intensified last night after Brussels insisted that any delay to the UK’s departure from the EU was conditional on parliament approving Theresa May’s plan.
The petition, which was uploaded yesterday, 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.”
Nicola Sturgeon was among the parliamentarians to share the petition.
“An issue as big and important as Brexit should not come down to petitions - that said, if you are frustrated that the PM is just not listening, you can sign here,” the First Minister said.
Edinburgh South MP Ian Murray also encouraged others to sign.
“Given the clock is ticking and the PM is still flogging her dead horse deal, you may wish to sign this,” he said.
“Revocation may be the only viable option remaining come next Friday to prevent a no deal.”
The Labour MP added he still did not think No Deal would be allowed to happen.
Last night, the prime minister claimed a second EU referendum was not something the people want and pointed to the first vote in 2016 which was “decisively” in favour of leaving the European Union.
Edinburgh North and Leith constituency has among the highest number of signatories to the petition anywhere in the UK, with over five per cent of voters having signed up.
SNP MP Deidre Brock said: “The Prime Minister’s handling of Brexit has been an absolute disaster – and, with just days to go, we’re still none the wiser as to what’s going to happen.
“The fact that more than a million people have now signed this petition speaks volumes. It’s essential that we press pause and go back to the people.
“We cannot accept the false choice that our only options are between the disaster of the Prime Minister’s deal or the catastrophe of a No Deal. But if parliament cannot agree on a way forward then we’ll seek to revoke Article 50.