US President Barack Obama and British Prime Minister David Cameron during a bilateral meeting.

US Secretary of State John Kerry is travelling to Brussels and London today for talks on the future of the European Union and the fallout arising from the June 23 Brexit vote.

A senior US official said that at the EU leaders meeting in Brussels Mr Kerry would stress the importance of other EU members not following Britain to further weaken the bloc.

Through a referendum held on June 23, citizens of the United Kingdom voted to leave the EU and Mr Kerry’s travel to the EU headquarters comes as the European Parliament’s chief urged UK Prime Minister David Cameron to begin formal proceedings to leave the EU as early as Tuesday.

EC Parliament Chief Martin Schulz
EC Parliament Chief Martin Schulz

Martin Schulz said that a period of uncertainty over Brexit would “lead to even more insecurity and thus endanger jobs”.

“Hesitating simply to accommodate the party tactics of the British conservatives hurts everyone,” he said.

“That is why we expect the British government to now deliver. The summit on Tuesday is the right time.”

The four biggest groups in the European Parliament are also reported to have drawn up a draft resolution calling for the Prime Minister to begin the process of the UK leaving the EU.

UK foreign Secretary Philip Hammond
UK Foreign Secretary Philip Hammond

But the Foreign Secretary Philip Hammond said: “There is no imperative on us to serve Article 50 at any particular time. We’re under pressure from our EU partners to do it quickly, but the timing is entirely up to us.”

One of the leading Brexit campaigners, Conservative MP Liam Fox, insisted talks should begin with the aim of the UK leaving the union by the beginning of January 2019.

“What we want to be doing is seeing a process that means we can leave the European Union on 1 January 2019. That seems to me like a reasonable timetable,” Mr Fox said.

The Prime Minister said in the wake of the referendum result that he would step down by October and leave negotiations on Brexit to his successor.

To begin the withdrawal process, Britain must invoke Article 50 of the EU’s Lisbon treaty, which has never been used before.

The EU’s summit on Tuesday and Wednesday will discuss the fallout from the British vote and the European Parliament will also hold a special session.

Mr Schulz’s demands came after German Chancellor Angela Merkel said there is no need to be ‘nasty’ during talks to discuss Britain’s exit.

She told a news conference it “shouldn’t take forever” for Britain to deliver formal notification that it wants to leave the European Union but made it clear that the matter is in London’s hands.