Arriving for a summit in Brussels, where Brexit has been sidelined by a bloc-wide row over migration, May insisted there had been "very good progress" so far.
![The cow trampled its victims (image used for illustrative purpose) [iStock]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'100'%20height%3D'100'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "The cow trampled its victims (image used for illustrative purpose) [iStock]")
But she acknowledged: "I think both sides are keen to continue that work at a faster pace than we have done up till now."
The aim remains to secure a deal by October, to give it time to be ratified ahead of March 2019 when Britain will formally leave the European Union.
But there is frustration among EU leaders that the talks have become stalled on the thorny question of how to avoid border checks between British Northern Ireland and EU member Ireland after Brexit.
May's government is also distracted by in-fighting over the future economic relationship with Europe.
"I would like our British friends to make clear their positions," said European Commission President Jean-Claude Juncker.
He repeated that the EU was working on the possibility that the talks collapse, saying: "We have to do it."
Dutch Prime Minister Mark Rutte said the Irish issue "has to be solved", adding: "I am not losing patience but time is getting shorter and shorter to come to an agreement."
He added: "I do understand it is difficult to come to an agreement within her cabinet and the UK parliament, but she has to."
Irish premier Leo Varadkar, who has been pressing the border issue, said he had hoped to make "more progress -- or any progress" by now.
"We all need to intensify our efforts now," he said, warning there could be no deal without a solution for Ireland.
He said Britain should have drawn up a proper Brexit plan two years ago, and now had to accept the compromises it should make.
"It can't be cherry-picking... (the EU has) laws and principles and they can't be changed for any one country, even a great country like Britain.
"Any relationship that exists in the future between the EU and the UK isn’t going to be one of absolute equals."
In a lighter moment, Belgian Prime Minister Charles Michel presented May with a World Cup football shirt, ahead of his country's clash with England Thursday.
May will briefly update the other 27 EU leaders on Brexit at dinner on Thursday, and they will discuss the issue without her on Friday.
She is expected to hold one-to-one talks with some fellow leaders on the sidelines of the summit and over the course of next week.
May will then gather her ministers at her country retreat Chequers to thrash out their differences, before publishing a so-called white paper detailing her proposals early in July.
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