Theresa May is to make a last ditch plea to the European Union to give ground and allow changes to the proposed Brexit deal that would allow her party’s MPs to back it.

The prime minister will give a speech saying that the actions of Brussels negotiators will have a material impact on the outcome of the critical vote next week.

Her intervention comes as her chief negotiator is expected to head back to Brussels on Friday in a bid to secure something which will allow the government to say it has won some kind of alteration.

The mood of cabinet ministers has been grim in recent days as negotiations have failed to create the kind of breakthrough for Ms May to win the support of Tory Eurosceptics and her DUP partners in government for her deal.

Speaking in Grimsby on Friday afternoon, the prime minister will say: “Just as MPs will face a big choice next week, the EU has to make a choice too.

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“We are both participants in this process. It is in the European interest for the UK to leave with a deal.

“We are working with them but the decisions that the European Union makes over the next few days will have a big impact on the outcome of the vote.”

Geoffrey Cox is attempting to win changes to the Irish backstop – an arrangement which, as it stands in the withdrawal agreement, would see the UK potentially trapped in an indefinite customs union if Britain and EU fail to agree a trade deal by the end of 2020.

Conservative backbenchers in the European Research Group of MPs and members of the DUP have said they can only back the withdrawal agreement in a crunch vote on Tuesday if the UK has a legally-binding route to leave the backstop.

If the prime minister has not secured any changes by Sunday night she will go into the vote on Tuesday asking MPs to take a decision on an agreement which is ostensibly the same as the one rejected by 230 votes in January.

But until now EU leaders and officials have refused to consider suggestions to solve the issue put forward by the UK.

Speaking on Thursday morning French Europe minister Nathalie Loiseau said there had been “no precise proposals” from the UK and that the EU side was still waiting for something workable to be brought forward.

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A European Commission spokesperson went on the record on Wednesday to say talks so far had been “difficult” and that “no solution” was in sight.

Sir Keir Starmer, Labour’s shadow Brexit secretary, said: “It’s becoming increasingly clear that Theresa May will not be able to deliver the changes she promised to her failed Brexit deal. This speech looks set to be an admission of failure.