May will hold talks with EU President Donald Tusk, and has already met with her Irish, Swedish and Polish counterparts at a summit on European social reforms in Gothenburg as a deadline looms for Britain to make enough progress to move on to trade talks in December.
"I look forward to the European Union responding positively to that so we can move forward together and ensure that we can get the best possible arrangements for the future that will be good for people in the United Kingdom and across the remaining EU27," May said.
European Commission President Jean-Claude Juncker told reporters Britain needed to do more if it hopes to unlock the the next phase of Brexit negotiations, on future trade relations and a transition deal, at a summit in Brussels on December 14.
"The clock is ticking. I hope that we will be able to come to an agreement as far as the divorce is concerned at the December council (summit) but work has still to be done," Juncker told reporters.
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Irish Prime Minister Leo Varadkar meanwhile struck a firm line, insisting there had to be progress on Dublin's demands that Brexit should create no "hard border" between British- ruled Northern Ireland and EU member Ireland.
"I think it's certainly possible that we can come to conclusions in December allowing phase two talks to begin. But, you know, if we have to wait until the new year, or if we have to wait for further concessions, so be it."
"It's 18 months since the referendum, it's 10 years since people who wanted a referendum started agitating for one, sometimes it doesn't seem like they've thought all this through," he said.