Arriving in Brussels to meet with her 27 European counterparts the PM said “most of the issues” in the draft withdrawal agreement had been resolved and that only the Irish border remained.
The Prime Minister said “everybody around the table” wanted an agreement and that “by working intensively over the next days and weeks I believe we can achieve” one.
“Now is the time to make it happen,” she added. “As I say a deal is in the interests not just of the UK but also the European Union.”
Many of the prime minister’s counterparts were blunter than she was about the prospects for an agreement, however – though none ruled out an eventual resolution.
“Today there will be no breakthrough,” said Dalia Grybauskaitė, president of Lithuania, on the doorstep of the meeting.
“We realise that the technical agreement of last week was not accepted in London.”
She said a deal would likely have to wait until “November and maybe even more summits because we are not yet in the final stage”.
Xavier Bettel, Luxembourg’s prime minister, said there was “still hope” for a deal, but added: “But there is also the possibility of a no-deal. We'll continue to work on a no-deal too. Even if we have an agreement here it doesn't mean that Westminster agrees."
Mark Rutte, the Dutch PM, said he was cautiously optimistic that a deal could be reached in the next few weeks.
But he added: “Unfortunately we thought that last Sunday we could have finalised agreement. Now we focus on preventing an hard Irish border, that will be the main issue debated tonight. I do not think it will be solved completely.”
He left open the door to more flexibility from the EU side, stating he would not block a longer transition if it was to find a “common solution”.
Chief EU negotiator Michel Barnier, arriving, said: "We need time, much more time, and we’ll continue to work in the next weeks calmly and patiently."
The Prime Minister is set to address leaders and give her take on Brexit talks, before they leave her to go for dinner without her.
Over dinner they will hear from their chief negotiator Michel Barnier and decide whether there is any point in holding a special summit in November to finalise a deal, or whether the horse has already bolted.
Donald Tusk, the European Council president, had describe the meeting as the "moment of truth" for Brexit – though the designation appears to have once again slipped further back into the calendar.
Talks over the Irish border hit a wall on Sunday after promising signs a resolution was close. Ms May is under pressure from eurosceptics at home not to commit the UK to a customs union with the EU to solve the issue – but also from Northern Irish unionists in the DUP who do not want the region treated any differently from the rest of the UK, despite its unique geographic location.
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