Arriving for a second day of summit talks in Brussels, May noted that both sides remained at odds over a "backstop" plan to avoid frontier checks in Ireland if and until a new trade deal could be signed. Her so-called Chequers plan has already been rejected both by the European Union and her own party and the prime minister has not even begun the process of spelling out which of the alternative available options she is willing to accept. Despite her appearance, any hopes of a Brexit deal breakthrough is as low as it has ever been in recent weeks.
John McDonnell has ruled out the notion of extending the Brexit transition period beyond March 29 2019.
European Union leaders then listened to chief negotiator Michel Barnier's assessment of the talks that broke down last weekend over the Irish border issue, where both sides have committed to avoiding a hard border on the island of Ireland. She is hemmed in by pro-Brexit members of her Conservative Party, who oppose any more compromises with the bloc, and by her parliamentary allies in Northern Ireland's Democratic Unionist Party, who insist a solution can't include customs checks between Northern Ireland and the rest of the United Kingdom.
There, EU leaders raised the possibility that the post-Brexit transition period, during which Britain would retain EU rules, could be extended by a year as a way to give London more time to agree the EU-UK customs deal it wants to solve the issue of the Irish border.
He said: "I think what's more likely is that dates will be suggested, but that there won't be a commitment to a new summit unless there is a signal from the negotiating teams that there is something to sign off on".
Tory MP Nadine Dorries said: "If Theresa May is asking for a longer transition period, she is stalling".
Today, Mrs May will have further bilateral meetings, having had talks on Wednesday with Jean-Claude Juncker, the European Commission President, Donald Tusk, the European Council President, Leo Varadkar, the Irish Taoiseach, and Emmanuel Macron, the French President. In a recent speech, the newspaper reports that Scotland's first minister Nicola Sturgeon called for Scotland to be allowed to stay a member of the EU's single market, should Northern Ireland obtain a special deal.
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The idea of extending the transition would be to give more time to negotiate a deal on future relations and find a formula to defuse the Irish border question.
A month after May's last meeting in Austria, when her rejection of European Union proposals created to avoid a revival of border tensions in Northern Ireland provoked angry reactions, her tone was much calmer, said European Union officials who were present.
But Mr Coveney made it clear that summit would not go ahead unless significant progress is made on the border issue. "This is going to be a hard time, but the whole Cabinet is digging in to get the best deal for this country". "They do not know themselves what they really want".
Any extension would cost billions of pounds in EU fees and leave Britain under European rules for nearly six years after the referendum result.
Business Insider reported last week that Leadsom, Mordaunt and Work and Pensions Secretary Esther McVey were all prepared to quit Cabinet if the prime minister did not change her plans for the Brexit backstop. "Without a clear vote in the European Parliament and without a clear vote in the British Parliament, it won't succeed in the end". "Ministers can not silence Parliament", he said. "MPs must be given the opportunity to scrutinise, consider and, where appropriate, amend any resolution the Government puts forward".