Dutch Foreign Minister Bert Koenders | Kena Betancur/AFP via Getty Images EU foreign ministers to London: We won’t wait for you U.K. Conservatives want a new leader to begin Brexit negotiations, but the other countries want to get on with it.

LUXEMBOURG — European Union foreign affairs ministers on Friday sent a stark message to the British government: We can't wait until October to begin divorce proceedings.

When David Cameron announced Friday morning that he was stepping down in the wake of the Brexit result, he said the decision on when to trigger Article 50 of the Lisbon Treaty — which starts the clock on talks to leave the bloc — should fall to his successor, to be in place by October. But EU ministers don't want to wait that long.

"The biggest issue to be discussed now is when the process of actual British disconnection from the European Union starts and the overwhelming feeling among the member states is that we simply cannot wait until the Conservative Party finds a new leader," Slovak Foreign Minister Miroslav Lajčák told journalists in Luxembourg.

“It was very clear from all sides that we should not stay in a vacuum,” Dutch Foreign Minister Bert Koenders said. ”You cannot have your cake and eat it.”

When asked how they will put pressure on the U.K. to speed up the decision, ministers replied that it is up to the British government to push the button on Article 50.

However, diplomats said decisions should be made with or without the Brits.

“Look, how many times has [European Council President] Donald Tusk repeated in his statement that now we are 27?” one EU diplomat said.

Meetings of the 27 have already been planned. On Sunday, representatives of the member countries — so-called sherpas — will meet to discuss the way ahead. On Monday, Tusk will meet French President François Hollande in Paris and German Chancellor Angela Merkel in Berlin before seeing Dutch Prime Minister Mark Rutte, whose country holds the rotating presidency of the Council, and the Czech Republic's Bohuslav Sobotka in Brussels.

Merkel will also meet with Hollande and Italy’s Matteo Renzi to prepare for a European leaders' summit on Tuesday and Wednesday, a diplomat said.

In a letter to EU leaders sent Friday evening, Tusk outlined the program for the summit: On Tuesday, Cameron will explain to EU leaders over dinner what happened in the vote, and on Wednesday the 27 other leaders will meet informally to discuss the political and practical implications of Brexit.

"First of all, we will discuss the so called 'divorce process' as described" in Article 50, Tusk wrote. "And secondly, we will start a discussion on the future of the European Union with 27 Member States.”

However, whether the European reaction involves setting up a two-speed Europe remains to be seen.

“We must recognize that a generic approach that says that Europe at 27 must push for further integration does not have legs,” Italian Foreign Minister Paolo Gentiloni said. However, he said there could be “an approach where ... some countries ... have a higher degree of integration."