UPDATED 10.48am Just days after voting to leave the European Union, more than 2 million Britons and UK residents have signed a petition calling for a second vote, forcing MPs to at least consider a debate on the issue.

Parliament has to consider a debate on any petition posted on its website that attracts more than 100,000 signatures.

The proposal, posted before the June 23 referendum, said the government should hold another plebiscite on EU membership if the support for Leave or Remain in a referendum was less than 60 per cent in a turnout of under 75 per cent of eligible voters.

The result on Thursday saw 52 per cent of voters, 17,410,742 people, back a British exit, on a turnout of 72 per cent.

Since then, the petition - which only British citizens or UK residents have the right to sign - was proving so popular that by 1725 GMT on Saturday, 2,005,101 people had signed it.

By late afternoon, it appeared to be rising at a rate of more than 3000 signatures a minute.

Most of those who signed were based in areas where support for staying in the EU was strongest, most especially London, the website indicated.

Prime Minister David Cameron, who said on Friday he would resign after leading the failed campaign to keep Britain in the EU, had said there would be no second referendum.

Scotland is already working on what it can do to stay in, when Britain quits.

Scotland's First Minister Nicola Sturgeon said people north of the border clearly don't want to leave.

"We will seek to enter into immediate discussions with the EU institutions and with other EU member states, to explore all possible options to protect Scotland's place in the EU."