European Council President Donald Tusk (C), European Commission President Jean-Claude Juncker (R) and Dutch Prime Minister Mark Rutte attend a press conference at the EU headquarters in Brussels, Belgium, June 28, 2016. European leaders on Tuesday pressed for a quick and clear British departure plan to quell worldwide anxiety about the continent's future. [Photo: Xinhua]

European Council President Donald Tusk said on Tuesday that the British Prime Minister, David Cameron, will take back a message to the United Kingdom from his EU counterparts that talks on a British exit from the European Union must start promptly.

Tusk said there was no legal way to push London towards a quick activation of the EU treaty's voluntary exit clause, known as article 50 in the treaty of Lisbon.

EU Commission President Jean-Claude Juncker has also urged Britain to notify the European Union regarding its withdrawal from the bloc it joined in 1973 as soon as possible.

"All those having campaigned for the 'leave', they are telling us: 'we need some time'. I thought that if you want to leave, you have a plan, you have a project, you have a global picture. They don't have it but I hope that the notification by the next British government will arrive as soon as possible."

Earlier in the day, the European Parliament adopted a non-binding resolution demanding that London activate article 50 as soon as possible.

Cameron has so far refused to trigger the withdrawal procedure, saying it will be up to his successor to take that decision. The leadership election is expected to take place in early September.

That would launch negotiations on withdrawal terms with a two-year countdown to departure.

For the first time, the other 27 leaders will hold their own meeting on Wednesday to discuss how to deal with Britain as it leaves the bloc, and how to take the Union forward without it.