Brexit talks to continue after May-Juncker meeting

She is pushing for tweaks to the so-called backstop, an arrangement that would keep Britain aligned with the EU's customs union to avoid a hard border on the island of Ireland.

"That's what is required if a deal is going to pass the House of Commons ... Time is of the essence," May said.

The EU has ruled out changes to the withdrawal agreement, but is willing to come up with annexes to the Brexit deal that could soothe concerns in the UK parliament.

Expectations were low in the EU on Wednesday's meeting, the second of its kind in two weeks, with EU officials and member states wanting to first see assurances that May can get a modified deal through parliament before they budge.

Discussions between Juncker and May focused on figuring out "which guarantees could be given with regard to the backstop that underlines once again its temporary nature and give the appropriate legal assurance to both sides", according to a joint statement.

They also touched on "the role alternative arrangements could play in replacing the backstop in future".

May said that her Brexit minister, Steve Barclay, would be back in Brussels on Thursday, along with British attorney general Geoffrey Cox, who has emerged as a key player on the UK side, as he holds the view the backstop could become a permanent state for the UK.

Negotiators are hoping to convince Cox that the EU does not intend to keep the backstop in place forever, but only until a better solution is found to keep open the border on the island of Ireland under a new deal on future British-EU relations.

Cox told British lawmakers in December that although the Brexit deal stipulated the backstop would be temporary and only apply until the two sides had settled their future relationship, there was no way for the UK to leave the arrangement without the approval of EU member states.

Changing Cox's legal advice could swing the necessary number of votes in favour of the Brexit deal in Westminster, negotiators hope.

The EU, however, argues that a time limit to the backstop, or a unilateral exit clause for the UK kills the purpose of the deal as an insurance policy.

In a joint statement, May and Juncker said they were working on "appropriate legal assurance to both sides".

Brexit looms

But with only 37 days until Brexit, the risk of a no-deal scenario is increasing.

The UK could ask for a delay on Brexit to negotiate further and to avoid running out of time to pass the necessary laws in the next month to prepare for its departure.

"Of course, if Britain fails to prepare some sensible option on time, then there is always a possibility to extend these negotiations in time. This would be better than a divorce without agreement," EU Council president Donald Tusk said in an interview on Wednesday.

May will meet with several EU leaders during a weekend summit with Arab governments in Egypt.

The EU leaders are also looking for assurances she can deliver parliamentary ratification for the deal before they agree to attach any new provisos to the Brexit accord.

The talks come as three Tory MPs left May's party to join a new "Independent Group" in parliament together with eight Labour MPs who broke away from Britain's main opposition party.

The three MPs criticised May's government for letting the "hard-line anti-EU awkward squad" take over the party, BBC reported.