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Leaders of the original six EU states have discovered a sudden need for speed when it comes to the British exit, reports ITV News correspondent John Ray.
They are demanding fast action while Britons process significant anger and domestic fallout from the unexpected vote to leave.
Britain should not rush to press the start button on a formal divorce from the EU, the chief executive of Vote Leave has said.
Matthew Elliot suggested that the UK should wait until autumn before invoking article 50 of the Lisbon Treaty, which will kick-start the process of exit.
Mr Elliot said the final deal should include agreements on the British contribution to the EU, access to the single market, extradition agreements and free trade "passporting" for financial services.
It comes after a European Central Bank boss warned that the UK could not expect all the benefits of EU membership unless it agreed to apply all the bloc's rules.
The European Commission's President has urged Britain to speed up "divorce" talks following the referendum result to leave the European Union.
Jean-Claude Juncker said exit negotiations should get "started immediately", adding that the EU would pursue a "reasonable approach".
"It's not an amicable divorce, but it was not exactly a tight love affair anyway," he told Germany's ARD television station.
Article 50 is effectively the rule-book on how to leave the EU.
Once triggered, we would have two years to negotiate our exit from the union, as ITV News' presenter Tom Bradby explains.
The leaders of the European Union have bared their teeth the day after Britain voted by a narrow majority to become the first member to leave the 28-member bloc.
ITV News Europe Editor James Mates reports on the angry response from Brussels, while far-right leaders across Europe urged their nations to put their membership to a public vote.
European Council president Donald Tusk will convene the first EU summit without Britain next week to discuss the impact of the Brexit vote.
An EU official confirmed Mr Tusk will host the leaders of the 27 other members of the bloc on Wednesday.
Mr Cameron is due to attend only the first day of a scheduled two-day EU summit on Tuesday before the leaders discuss Britain's exit the following day.
Mr Tusk earlier joined senior EU representatives in issuing a direct challenge to Britain to implement the terms of its Brexit "as soon as possible, however painful that process may be".
Senior EU representatives have issued a direct challenge to Britain to implement the terms of its Brexit "as soon as possible, however painful that process may be".
Vote Leave leaders Boris Johnson and Michael Gove earlier said there was "no need for haste" in invoking the Clause 50 process to trigger Britain's formal two-year withdrawal.
But a joint statement, led by European Council president Donald Tusk and European Commission president Jean-Claude Juncker warned "any delay would unnecessarily prolong uncertainty".
Turkey's prime minister has called on the EU to "reconsider its vision" in the wake of Britain's exit the EU referendum as world leaders and even the Pope responded to the historic vote.
Binali Yildirim said European leaders should read the Brexit vote properly as he continued to press for his nation's admittance into the member bloc.
The issue of Turkey's potential future entry into the EU formed a key dispute between the Vote Remain and Vote Leave campaigners in the build up to Thursday's historic vote.
Pope Francis meanwhile said Britain's EU exit was the "will expressed by the people" but must be followed by "guarantees" for the good of both Britain and countries on the continent.
South African president Jacob Zuma said his country could withstand the financial shocks caused by the Brexit.
Zuma said the treasury and central bank were in talks with financial institutions on the possible implications on Africa's most industrialised country.
German chancellor Angela Merkel has said it must the goal for the European Union to maintain "close future relations" with Britain as she confirmed she will hold a summit of leaders on Monday.
Mrs Merkel said she will meet with the European Council president Donald Tusk, French president Francois Hollande and Italy's prime minister Matteo Renzi in Berlin on Monday.
The German leader said she "deeply regrets" the decision of a majority of British voters at the ballot box to split from the 28-member bloc.
But amid apparent anxiety from other leaders, she said Europe needs to stay "calm and composed" in the wake of Britain's exit.
Latest ITV News reports
Foreign Secretary Philip Hammond said there will have to be a "trade-off" on UK access to the EU single market and migration controls.
France's foreign minister called for the UK to trigger the exit clause after a meeting with counterparts of the six EU founding states.