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8 year oldJean-Claude Juncker, President of the European Commission, said anyone wanting access to the EU's market must adhere to criteria "without exception".
There could be "no negotiation without notification", he said.
The German and French leaders and European Council President Donald Tusk said the same.
Mr Tusk said there would be another meeting of EU leaders, excluding the UK, on 16 September in Bratislava to discuss so-called "Brexit".
German Chancellor Angela Merkel also reiterated that there would be no discussions with the UK until Article 50 was formally triggered by the UK government.
"We wish that that would happen as soon as possible," she said.
On Tuesday, UK Prime Minister David Cameron said the rest of the EU wanted to have the "closest possible" relationship with the UK after Brexit.
But he said immigration was a "great concern" among UK voters and squaring this with access to the EU single market would be a "huge challenge".
The Hungarian Prime Minister, Viktor Orban, said that Mr Cameron told EU leaders at Tuesday night's dinner that the "lack of a decisive and effective method to handle migration" had led the majority of British voters to choose to leave the EU.
The principle of freedom of movement of people is one of the "four freedoms" - along with goods, capital and services - that underlie the EU's internal market.
EU leaders seem united after Wednesday's meeting that there will be no "nuances", as Mr Juncker put it, for the UK.
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