British Prime Minister David Cameron (L) is welcomed by European Commission President Jean-Claude Juncker (R) prior to a meeting in Brussels, Belgium, 28 June 2016.

Britain's outgoing Prime Minister David Cameron was set Tuesday to have difficult summit talks with his European Union counterparts over the timing and terms of his country's momentous referendum decision to leave the bloc.

Thursday's vote, paving the way for one of the EU's top three economies to take the unprecedented path of leaving, has triggered political mayhem in Britain, caused global market panic and sent shock waves across the EU.

"While we are leaving the EU, we mustn't turn our backs on Europe. These countries are our neighbours, our friends, our allies, our partners," Cameron, who resigned over the referendum outcome, said as he arrived in Brussels.

Britain's exit talks should be "as constructive as possible" and, once out of the bloc, the country should aim for "the closest possible relationship in terms of trade and cooperation and security," Cameron added.

But the British leader was facing criticism for leaving to his successor - due to be elected in September - the responsibility of starting the process by activating Article 50 of the EU treaty, rather than initiating divorce proceedings immediately.

"We are not on Facebook where the status is 'complicated,'" said Luxembourg Prime Minister Xavier Bettel ahead of the Brussels summit. "Either you are married or divorced, but not something in between."

"I don't intend to accept that we are subjected to blackmail inflicted by Britain," added his Belgian counterpart Charles Michel.

EU foreign policy chief Federica Mogherini said it was not even clear whether Britain really wanted out.

"The British people were quite clear on this, but we are receiving contradictory messages from ... a rather confused political scene in London," she said.

Earlier, European Commission President Jean-Claude Juncker told the European Parliament, "I would like the United Kingdom to clarify its position, not today, not tomorrow at 9 am, but quickly."

But Dutch Prime Minister Mark Rutte said there was no point in giving Cameron "a bollocking" as his country was reeling from the shock of Brexit, which has also called into question national unity, as pro-EU Scotland has threatened to secede.

"I'd say give them some leeway. I told you that now [Britain] has collapsed, politically, monetarily, constitutionally and economically. ... Let them get their political house in order," Rutte said.

British leaders have also been warned that they cannot expect easy access to EU membership benefits once they walk out.

"Whoever leaves the family can't expect the same privileges as it had before without also having the obligations," German Chancellor Angela Merkel said at a pre-summit parliament debate in Berlin.

She reiterated that there would be no discussions with Britain, formally or informally, on the framework for leaving the EU until London officially invokes Article 50, which launches a two-year window to reach an exit agreement.

Meanwhile, Juncker said he issued a presidential order banning all EU commissioners from discussing Brexit with London officials for the time being, to avoid any "secret negotiations in dark rooms, with curtains drawn," taking place.

EU leaders were scheduled to exchange views with Cameron over dinner, after clearing other summit agenda items - including migration and foreign policy - and meetings with European Parliament President Martin Schulz and NATO Secretary General Jens Stoltenberg.

The summit is due to continue Wednesday without Britain, with the remaining 27 EU nations planning to hold informal talks to seek a common position on Brexit and launch a discussion on strengthening their bloc.

Signalling that this week's meetings would not be decisive, EU President Donald Tusk called another summit in September. The meeting will not include Britain, an EU source said.

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