The European Parliament overwhelmingly passed a motion warning that “sufficient progress has not yet been made” on agreeing the divorce deal.
EU leaders have insisted Britain must first move to settle three key separation issues: the financial settlement, the future rights of EU citizens and the Irish border.
But the motion – passed unamended – instead accused the UK of having “seriously impeded” talks over the divorce bill because of a lack of “clear proposals”.
The resolution was backed by 557 MEPs sitting in Strasbourg, with just 92 voting against and 29 abstentions.
Only a “major breakthrough” should see the EU council of ministers agree to move onto the second phase of the talks – future trade – at a summit later this month, it said.
The vote in Strasbourg is not binding, but the views of MEPs are crucial because they have a veto over any final Brexit agreement.
It represents a setback for the Prime Minister, who hoped her speech in Florence – promising to plug any hole in the EU budget, until 2020 – would break the stalemate.
During the debate, a senior MEP warned Ms May that Boris Johnson must be sacked if she wanted to prevent the Brexit negotiations breaking down.
Manfred Weber, a key ally of German Chancellor Angela Merkel, said the Foreign Secretary’s interventions left the Government “trapped by their own party quarrels and political contradictions”.
“Please sack Johnson because we need a clear answer who is responsible for the British position,” said the leader of the centre-right EPP grouping in the European Parliament.
“Who do I call in London – Theresa May, Boris Johnson or David Davis? Please don’t put your party first. We need a clear answer who is responsible for the British position.”
The warning was echoed by Guy Verhofstadt, the Parliament’s Brexit coordinator, who said cabinet splits were blocking progress in the exit talks.
“There is a lack of clarity, there is even disunity,” he said. “There are oppositions between [Philip] Hammond and [Liam] Fox. There are divisions between Johnson and May.”
MEPs made clear they will veto any deal unless Britain continues to accept European Court of Justice rulings during any implementation period.
“Such a transitional period can only be envisaged under the full jurisdiction of the Court of Justice of the European Union,” the motion said – and if other withdrawal issues are “concluded”.
However, ending the jurisdiction of the court immediately at the point of Brexit was one of the four red lines set out by the Foreign Secretary over the past weekend.
He also demanded that no new EU directives or regulations should apply to Britain after Brexit and that the UK should not pay, or accept EU rules, to gain long-term access to the single market.
Some senior Tories believe that Mr Johnson is deliberately attempting to set Ms May up to fail by making demands that Brussels will never agree to.
MEPs passed the resolution, drawn up by the Parliament’s Brexit Steering Group, following a debate on Tuesday morning with EU Commission President Jean-Claude Juncker and chief negotiator Michel Barnier.
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