There is only a slim chance that an agreement between British and European Union negotiators can be reached in time to hold a summit of leaders in November to sign off the agreement, according to one British official.
Mrs May updated European Council president Donald Tusk on the situation on Wednesday morning.
The European Union's Brexit negotiator, Michel Barnier, today said it is impossible to say when divorce talks with Britain would be finalised and that there would be no deal agreed without a solid fix for the Irish border.
"I believe it possible to reach an agreement in November, but every day that passes lessens the possibility of having an extraordinary summit in November", said the irish Prime minister Leo Varadkar, also in Helsinki on Wednesday.
The issue of the Irish border - and how to avoid customs checks that could undermine the Northern Ireland peace deal - has forced the negotiations into an impasse.
A Downing Street source said: "That is just where we are so far".
"But we do have one scheduled anyway for the 13th and 14th of December, so not getting it done in November doesn't mean we can't get it done in the first two weeks of December", he added.
"We will have to fight against those who want to demolish Europe with their fear, their populist deceit", he told more than 700 EPP delegates in Helsinki, before naming the former Ukip leader Nigel Farage.
In a wide-ranging speech that moved from European defence to electric vehicles, he mentioned Brexit only to promise to "fulfill my Brexit mission to the end" and make a brief opening joke that his speech would be short because "the clock is ticking". I will not give you a date. "The choices need to be made now on the United Kingdom side", he told reporters.
May told her cabinet on Tuesday that more time was needed to clear the final hurdle standing between her and a deal: the plan to ensure no hard border emerges on the island of Ireland.
May has said no British prime minister could agree to such a concession, but negotiators are reported to be working on language for a "review mechanism" that would govern the backstop. "It's as simple as that", explained Michel Barnier after a meeting on Tuesday evening with the Prime minister of slovakia Peter Pellegrini in Bratislava.
Later, addressing leaders of the European People's Party group, Barnier warned of the threat that rising nationalism and populism pose to the EU ahead of European Parliament elections in May.