BRITAIN should implement Brexit “as soon as possible”, Brussels chiefs have insisted, as the decision to quit the European Union sent shockwaves across the continent and beyond.

In his resignation speech, David Cameron made clear there would be no rush to begin the official two-year divorce process under Article 50 of the 2007 Lisbon Treaty.

The negotiation with the EU, the Prime Minister explained, would need to begin under his successor, who would not take over until the autumn.

Donald Tusk, the European Council president, Martin Schulz, the European Parliament president, Mark Rutte, the prime minister of the Netherlands, which currently holds the rotating presidency of the European Council, and Jean-Claude Juncker, the European Commission president, made clear they wanted a swift resolution to Brexit, warning that "any delay would unnecessarily prolong uncertainty".

However, leading Brexiters like Boris Johnson, now favourite to succeed Mr Cameron as Tory leader and PM, energy minister Andrea Leadsom and former defence secretary Liam Fox, have made clear they do not want to rush things. Mr Johnson insisted there was “no need for haste”.

With elections in France and Germany next year, it is thought stretching out proceedings could give the new PM more political leverage.

In a joint statement the EU’s presidents expressed regret at the UK’s decision to leave the EU but stressed they respected it.

They made clear EU law "continues to apply to the full, to and in the United Kingdom, until it is no longer a member" and stressed that the concessions agreed as part of Mr Cameron's renegotiation, such as on welfare, would now be abandoned.

They said they hoped the UK would remain "a close partner of the European Union also in the future" but that the EU would "stand strong and uphold the EU's core values of promoting peace and the well-being of its peoples" as a 27-nation bloc. Mr Juncker stressed how there was no possibility of a second renegotiation.

Christine Lagarde, the chief executive of the International Monetary Fund, urged the authorities in the UK and Brussels to work on a "smooth transition" to a new relationship amid fears about the economic impact of Brexit.

Responding to Britain’s decision, governments across the EU held emergency sessions.

Angela Merkel, the German chancellor, expressed “great regret” at Britain’s decision and invited Mr Tusk, French president Francois Hollande and Italian premier Matteo Renzi to a meeting in Berlin on Monday ahead of a previously scheduled EU summit when Mr Cameron will explain to his EU counterparts the background to the Brexit decision.

"The European Union is strong enough to find the right answers to today," declared Mrs Merkel.

Mr Hollande admitted the UK's Brexit vote had "seriously put Europe to the test", stressing how it should act as a "jolt" to the bloc to ensure "profound change" was implemented to address its troubles.

Mariano Rajoy, the Spanish Prime Minister, said his country had "solid economic foundations" to deal with the financial "turmoil" that could follow Britain's decision to quit the EU.

Radoslaw Sikorski, who was in the elite Bullingdon Club with Boris Johnson during their time at Oxford University, tweeted after the Brexit vote was made official: "David, Boris, what have you done?!"

Estonian Prime Minister Taavi Roivas said: "We must...work hard so that we do not lose the unity of the European Union," while Portuguese President Marcelo Rebelo de Sousa said: "The European project remains valid to defend the values that mark our common identity."

Witold Waszczykowski, the Polish foreign minister, said the Brexit result showed “disillusionment with European integration and declining trust in the EU”. He sought to reassure the 850,000-plus Poles living in Britain that “during talks… we will aim to guarantee the rights citizens have acquired”.

Meantime, Brussels is now on alert for a wave of copycat national polls across the EU.

Right-wing leaders across the 28-member bloc were swift to underline their demands for similar votes following the shock result.

Marine Le Pen, the leader of the National Front in France, tweeted "victory for freedom", adding that she had "asked for years" for the same process to be held in all EU nations.

Geert Wilders, who heads the populist PVV party in the Netherlands, said Dutch voters should be given a say on membership as soon as possible.