The EU has warned that it will not renegotiate the Brexit withdrawal agreement - regardless of who becomes the next Prime Minister.
Jean-Claude Juncker, the European Commission president, said the bloc's leaders were in agreement that the current deal, which has been rejected three times by the UK parliament, should not be reopened.
Speaking after a meeting in Brussels with EU leaders - excluding outgoing prime minister Theresa May - Mr Juncker said: "We repeated unanimously that there will be no renegotiating of the withdrawal agreement."
Mrs May's Brexit deal had come under fire from MPs on a range of issues, including the backstop, the Irish border and how much money the UK owes the EU.
European Council president Donald Tusk added that a prime ministerial change could make the process more "exciting".
He said: "We are waiting for the new British prime minister and we have to be very precise and also patient.
"It's waiting for the decisions or maybe new proposals, but our position remains as I informed just five minutes ago.
"Maybe the process of Brexit will be even more exciting than before because of some personnel decisions in London, but nothing has changed when it comes to our position."
Britain is due to leave the bloc on October 31 after it was granted an extension from its original leave date of March 29.
However Mrs May's resignation and the subsequent Conservative leadership contest means time is wasting away in the countdown to the UK's departure.
Other EU leaders said any extension should only be granted if there were a general election or another referendum on the EU vote.
"It's not possible (that) because you change the leader in the UK that we need to postpone decisions," said Luxembourg Prime Minister Xavier Bettel.
The head of the Bank of England on Friday dismissed suggestions from Tory leadership frontrunner Boris Johnson that tariffs on trade with the EU can be avoided even if the country leaves the bloc without a withdrawal agreement.
Mr Johnson said Britain can rely on a provision in international trade rules to make sure trade relations remain unchanged.
But Mr Carney said that was not possible if there was no deal between the EU and Britain.
Mr Carney said the UK would automatically be hit by tariffs as the Europeans would have to apply the same rules to Britain as every other country outside the tariff-free EU.
"If they were to decide not to put in place tariffs, they will also have to lower tariffs with the United States, with the rest of the world," he said. "And the same would hold for us."
Carney indicated there's only so much firms can do to offset the impact of tariffs. Three-quarters of firms, he said, have done as much as they can, which in some cases may not be much.