It comes after Germany, France and Italy insisted the European Union will not hold informal talks with Britain until it triggers Article 50 of the Lisbon treaty, the mechanism under which members can leave.
British Prime Minister David Cameron says the country will not be rushed into negotiations to withdraw from the European Union.
In his first address to MPs since his resignation following the referendum to leave the EU, Mr Cameron said it would be for his successor to decide when to begin the formal exit process.
He said Britain needs to decide what kind of new relationship it wants before it triggers Article 50 of the Lisbon Treaty, to leave the EU.
"Before we do that we need to determine the kind of relationship we want with the EU and that is rightly something for the next prime minister and their cabinet to decide. I've also made this point to the presidents of the European Council and the European Commission and I'll make this clear again at the European Council tomorrow. Mr. Speaker this is our sovereign decision and it will be for Britain and Britain alone to take."
But speaking at talks hosted by German Chancellor Angela Merkel in Berlin, French President Francois Hollande said the process needs to begin without delay.
"Why shouldn't we waste time? Because nothing is worse than uncertainty. Uncertainty gets in the way of political and financial decisions which may as a result become irrational. The United Kingdom has in fact had experience of this both politically and financially. But there shouldn't be consequences on Europe, because Europe is solid, it is strong."
Following the referendum result, police across the UK are investigating claims of racism and hate crimes.
Romanian migrant Oana Gorcea told Sky News she was sent a racially abusive message after the referendum result was announced.
"'You're Romanian and are a visitor to the UK, shame on you, go to Germany and hedge your bets there.' I've never ever felt anything but at home up until Friday and, like a switch, it just changed. People woke up on Friday to a completely different world. I want that (other) world back. I want the Britain that I knew. I want my friends back."
Mr Cameron has condemned the racially-motivated attacks, telling MPs in parliament Britain must stand up for its values.
"In the past few days we've seen despicable graffiti daubed on a Polish community centre. We've seen verbal abuse hurled against individuals because they're members of ethnic minorities. Let's remember, these people have come here and made a wonderful contribution to our country."
Meanwhile, billions more dollars have been wiped off the value of shares in Europe since the British referendum.
And ratings agency Standard & Poor's has stripped the United Kingdom of its top credit rating, from AAA to AA.
The agency says the referendum "will lead to a less predictable, stable and effective policy framework in the UK."
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