"Leaders made it crystal clear that access to the single market requires acceptance of all four freedoms including the freedom of moment", said Donald Tusk, the President of the European Council, referring to the free movement of goods, services, capital and people.
The former Polish premier stressed that negotiations on Britain's future relationship with the European Union can not start until it formally triggers the two-year process leading to a divorce.
Barack Obama has warned European leaders to "catch their breath" and make plans for Britain's exit from the EU.
The freedom of movement is thought to have been among the sticking points for the Leave camp, which before the referendum argued the United Kingdom would be able to contol its borders in a more assertive manner if it left the EU.
Each of these nations is outside of the European Union but has access to the single market, which comprises the 440 million people and businesses within the 27 European Union states.
Germany's Angela Merkel said the European Union must "respect the result" of the vote.
Draghi had added that he agreed with private economists who predict euro zone growth will be reduced by up to 0.5 percent cumulatively over the next three years due to the Brexit vote.
"I cannot imagine that this emergency brake can be a principled thing", she said.
But Mr Juncker said that while reforms were needed, there would be "no treaty change".
However, in a clear rebuttal to the former mayor of London's claims, German Chancellor Angela Merkel warned on Tuesday that free access to the single market would mean losing some degree of control over immigration - a move that would anger many Brexit voters.
Tusk also maintained that he hoped the UK's withdrawal from the EU would be "orderly", adding that all 27 European leaders stressed their desire to remain united.
"We can not be embroiled in lasting uncertainty", Juncker said in a speech to the European Parliament, which he interrupted to ask British members of the assembly who campaigned to leave the EU why they were there.
The only real quantifiable detail in the article is a provision that gives negotiators two years from the date of article 50 notification to conclude new arrangements.
Mr Corbyn told the PM that Thursday's vote was a rejection of "a status quo that has failed", and urged him in response to scrap the so-called Bedroom Tax, ban zero-hours contracts and cancel Universal Credit cuts before his departure from 10 Downing Street in September.
It is hard to predict what exactly may occur while the Brexit ball keeps rolling but it does appear that Scotland will hold a referendum for independence and many think this situation brings the potential for the re-unification of Ireland.
"Of course everyone wants to see a clear blueprint in terms of what Britain thinks is right for its future relationship with the European Union". She said that combating youth unemployment, for example, could involve both scrapping EU directives and deepening European cooperation. While the decision to trigger secession talks lies with Britain, and they can wait until a new prime minister is in place, "it would be preferable to do this quickly so as to avoid entering into a prolonged period of uncertainty".
Shortly after the announcement of the "Leave" outcome, Prime Minister David Cameron, who had strongly campaigned to stay in the European Union, announced that he would step down.
"We regularly meet with regional leaders", said John Schranz, Schulz's spokesman.