Speaking on Thursday evening at a working dinner of butternut gnocchi and pheasant supreme with her Continental counterparts, the PM underlined the “difficult political background” she faces if she returns home empty-handed.
Referring to her September speech in Florence, she said: “I took stock, listened to what the people in the UK were saying, and what my friends and partners in Europe were saying, and I made a step forward.
“There is increasingly a sense that we must work together to get to an outcome we can stand behind and defend to our people,” she said, adding that when the 27 remaining member states convene tomorrow to discuss Brexit in private “the clear and urgent imperative must be that the dynamic you create enables us to move forward together”.
German Chancellor, Angela Merkel, appeared to have taken the hint when she told reporters suggestions from some in Britain that talks should be broken off were “absurd”.
She added: “In contrast to how it is portrayed in the British press, my impression is that these talks are moving forward step by step.
“I have absolutely no doubts that if we are all focused ... that we can get a good result. From my side there are no indications at all that we won’t succeed.”
Earlier during the dinner May sought to calm fears that Britain would use its departure in March 2019 to undercut the bloc’s economy by lowering standards and taxes.
She asked EU leaders to respond in kind to her efforts to break the Brexit stalemate, making clear she was disappointed at their plan to announce on Friday that talks have not yet made enough progress to move on to a discussion of future trade ties, reports Reuters.
In a rare tweet, banking boss Lloyd Blankfein sang the praises of Frankfurt - Germany’s financial centre - adding that he would be “spending a lot more time there”.
The EU is seeking a clearer commitment from Britain that it will settle financial obligations linked to its exit.
Leaders will on Friday set a target of December for London to improve its divorce settlement offer.
Back in the UK earlier this week, May issued a direct message to three million EU citizens living in Britain, promising she will make it as easy as possible for them to stay after Brexit.
In an open letter posted online and mailed to 100,000 EU nationals, Mrs May said the Government and Brussels are “in touching distance” of a deal on citizens’ rights and promised to involve EU expats in the design of a “streamlined” digital process for registering to remain.
And she repeated her message that “EU citizens living lawfully in the UK today will be able to stay”.
In response, EU nationals living in Britain said May “can do better” than her letter promising the Government will make it as easy as possible for them to stay after Brexit.
Campaign group the3million, which represents EU nationals in the UK, called on the Prime Minister for an “open dialogue about the real issues”.