A petition calling for a second EU referendum vote has now been signed by more than a million people.
Angry Remain voters have flocked to the Government’s website calling for a re-run of the ballot.
The Brexit campaign won Friday's vote with a 52 per cent majority but many of the UK’s major cities backed staying in the EU.
The petition states: “We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60% based a turnout less than 75% there should be another referendum.”
Leave wins EU referendum - in pictures
A House of Commons spokeswoman earlier said the site had temporarily been taken out of action due to "exceptionally high volumes of simultaneous users on a single petition, significantly higher than on any previous occasion."
"UK Parliament and the Government Digital Service are aware of the issue and are working hard to resolve the problems as quickly as possible."
The parliamentary petitions system is overseen by the Petitions Committee, who consider whether petitions that receive more than 100,000 signatures should be raised in the house. The committee is due to sit again on Tuesday.
A Change.org petition calling on Mr Khan to instigate the secession of London from the rest of the UK had passed 100,000 signatures by Saturday morning.
The page, set up by James O'Malley, stated: "London is an international city, and we want to remain at the heart of Europe.
"Let's face it - the rest of the country disagrees. So rather than passive aggressively vote against each other at every election, let's make the divorce official and move in with our friends on the continent.
Foreign ministers from the six founding members of the EU held a crisis meeting this morning to discuss the repercussions of the Brexit vote.
EU officials have called for the UK to exit the union as soon as possible to avoid any more complications.
France’s foreign minister Jean-Marc Ayrault said there would be a lot of pressure on David Cameron at the next EU summit on Tuesday to speed up the process of leaving.
Aides of Labour leader Jeremy Corbyn have denied he is on the verge of resigning following the referendum.
Mr Corbyn has been blamed by Labour Mps for not campaigning enough to try and keep Britain in the EU.
A motion of no confidence in the Labour leader has been submitted and will be discussed at the next Parliamentary Labour Party meeting on Monday.
