Signatories are calling for a new rule to be implemented stipulating that polls on the European Union with a majority under 60 per cent and turnout under 75 per cent must be re-started.
The petition started by William Oliver Healey, reads: “We the undersigned call upon HM Government to implement a rule that if the Remain or Leave vote is less than 60 per cent based a turnout less than 75 per cent there should be another referendum.”
It passed the million mark on Saturday morning, with votes most concentrated in London, Brighton, Oxford, Cambridge and Manchester.
The pattern largely followed that of the strongest votes for Remain in Thursday’s referendum, which ended with a result of 48 per cent, to 52 per cent for Leave, on a turnout of 72 per cent.
Such was the petition’s popularity on Friday morning that it crashed the government’s website, and its popularity means that it must be considered for a Parliamentary debate.
It was unclear if such a rule, if created and inserted into UK legislation, could be applied retrospectively.
Brexit reactions – in pictures
Brexit reactions – in pictures
Supporters of the Stronger In campaign look at their phones after hearing results in the EU referendum at London's Royal Festival Hall
Leave supporters cheer results at a Leave.eu party after polling stations closed in the Referendum on the European Union in London
Mr Cameron announces his resignation to supporters
Donald Tusk proposes that the 27 remaining EU member states ‘start a wider reflection on the future of our union’
Ukip leader Nigel Farage greets his supporters on College Green in Westminster, after Britain voted to leave the European Union
Supporters of the Stronger In Campaign react as referendum results are announced today
Boris Johnson leaves his home today to discover a crowd of waiting journalists and police officers
Leave EU supporters celebrate as they watch the British EU Referendum results being televised at Millbank Tower in London
Supporters of the Stronger In Campaign react as results of the EU referendum are announced at the Royal Festival Hall
Supporters of the Stronger In campaign react after hearing results in the EU referendum at London's Royal Festival Hall
Some were interpreting the petition to mean there was a pre-existing rule that could be applied to the result, although The Independent understands that no such provision exists in British or European legislation.
When a Remain vote was considered likely in May, Nigel Farage suggested he would support a second referendum if his side lost by a narrow margin.
The Ukip leader told the Mirror: “In a 52-48 referendum this would be unfinished business by a long way. If the Remain campaign win two-thirds to one-third that ends it.”
He made no mention of the sentiment on Friday, when he triumphantly hailed “independence day” for Britain.
David Cameron's office slapped down Mr Farage's suggestion at the time, with a tweet from the Prime Minister's official account reading: “The Leave campaign is wrong to say there'll be a 2nd referendum if we vote to remain in the EU. This is a referendum and not a neverendum.”
After the Scottish independence referendum in 2014, the 45 per cent of voters who lost started a similar campaign for another vote, and could now get their wish after Nicola Sturgeon said there had been a “significant change” to the circumstances of the original poll.