Discussions with Jeremy Corbyn do not appear to be making any progress with minister Dr Liam Fox warning Mrs May that the customs union with the EU Labour is demanding would be the "worst of both worlds" and EU leaders are growing exhausted of repeated extension requests.
Earlier in the day, Mrs May met Germany's Angela Merkel at her riverside Chancellery, a short walk from the Brandenburg Gate, and departed with a warm exchange of kisses.
At a tense meeting in Downing Street, Eurosceptic Cabinet ministers expressed their dismay over the links with Mr Corbyn and the prospect of a lengthy delay to Brexit.
But EU government heads with whom power actually resides, and notably President Macron of France, legitimately fear that in practice a delay of a year would simply mean Brexit uncertainty squeezing out all other EU work till long after we're all dead.
"The withdrawal agreement is not open for renegotiation", Barnier said, adding the EU would be ready to update the accompanying draft declaration on future EU-U.K. ties, should May's talks with the opposition Labour party move towards a customs union.
And he said to Labour MPs who support the Bill: "Understand the damage you are doing to this institution".
They want to know, if they say, "Yes", to another Brexit extension, what it will be used for.
Meanwhile, the government has taken steps to ensure the United Kingdom can take part in European Parliament elections on 23 May. He said the United Kingdom needed to show "substantial steps" towards resolving its political deadlock but said a no-deal Brexit would be the worst possible outcome.
The Prime Minister outlined the steps the government is taking to bring the Brexit process to a successful conclusion, and updated Chancellor Merkel on the ongoing discussions with the Opposition.
One of most contentious parts of the plan is the Irish backstop - an insurance policy that aims to prevent the reinstatement of a hard border on the island of Ireland.
Labour's shadow business secretary Rebecca Long Bailey said they were "hopeful progress will be made".
British MPs on Monday passed a new law aimed at preventing a no-deal Brexit this week by obliging the government to ask European Union leaders for a delay.
If no compromise can be reached between the parties, Mrs May has committed to putting a series of Brexit options to the Commons and being bound by the result.
Mr Gauke played down a report that Mrs May was considering offering MPs a vote on whether to hold a confirmatory referendum on any Brexit deal that was agreed.
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The foreign minister responded by taking a shot at the USA relief efforts from hurricanes Harvey, Michael and Florence and Maria. Around 70 villages in the province have already been evacuated in the past week.