Mrs May stepped down as Conservative Party leader on Friday, but will remain as Prime Minister until a replacement is elected, expected to be before the end of July. Several leading Tories vying to replace her, including Boris Johnson, Jeremy Hunt and Dominic Raab, have vowed to return to Brussels and secure better terms. Theresa May’s Brexit deal already resoundingly been rejected three times by Parliament as the impasse over the UK’s departure from the European Union continues.
He told a press conference on Friday evening: “A new Prime Minister will not change the problem.
“The problem is there and the new Prime Minister will have the responsibility with us to solve this problem.
“We are ready to engage with him and his team. We are ready to work once again for an orderly Brexit.”
Brussels has said it is open to redrafting the political declaration, which outlines the terms of future trade talks between the UK and EU.
But this will only happen if Britain relents on some of its red lines and opts for a closer relationship with the bloc.
Mr Barnier repeated the EU’s insistence that the backstop, which has been the primary obstacle in the Brexit deal being voted through Parliament, could not have a time limit.
Slovakia’s Foreign Minister Miroslav Lajčák, who appeared alongside Mr Barnier at the press conference, insisted the EU would only agree to another Brexit extension if there was going to be a general election or second referendum.
He said: “Definitely not because someone has given a promise to reopen the withdrawal agreement.
“Some of them are already promising that they will force the EU to reopen the withdrawal agreement. It will not happen.”
He added: “The new leader will inherit the same divided country, the same Parliament which has rejected all the possible deals so far and will inherit the same arrangement.”
EU leaders will be given an update on the Brexit progress at a summit in Brussels later this month.
They could decide on a possible request for another Brexit extension at a different meeting closer to the October 31 no deal deadline.