Theresa May vows to deliver Brexit agreement 'on time'

British Prime Minister Theresa May vowed to deliver an on-timeBrexit agreementfollowing talks with European Union leaders in Brussels on Thursday.

"I am clear that I am going to deliverBrexit," she said. "I am going to deliver it on time, that is what I am going to do for the British public. I will be negotiating hard in the coming days to do just that."

May said she saw and heard a desire from EU leaders to ensure Britain leaves the bloc with a deal.

"What I see and hear from leaders is a desire for us to work together to ensure that we can deliver the U.K. leaving the European Union with a deal," May said after meeting European Commission President Jean-Claude Juncker and European Council President Donald Tusk.

"It is not going to be easy but crucially President Juncker and I have agreed that talks will now start to find a way through this, to find a way to get this over the line and to deliver on the concerns that Parliament has so we get a majority in Parliament," she said.

Earlier, Juncker's spokesperson,Margaritis Schinas, saidthat he "underlined that the EU 27 will not reopen the withdrawal agreement, which represents a carefully balanced compromise."

Schinas saidMay "raised various options" for getting around the main sticking point in the Brexit negotiations, the backstop arrangement to avoid checks on the Irish border.

Describing the approximately 90-minute meeting between the European Commission's presidentand May as "robust but constructive," Schinas said the EU and Britain have already "made significant concessions to get a deal."

May and Juncker are due to meet again before the end of the month.

European Parliament President Antonio Tajani, who also met with May on Thursday, warnedthat the EU and Britain are on the verge of an "economic and human catastrophe" if they fail to finalize the Brexit agreement.

"We are very concerned.... This is the reality of a no-deal Brexit," he said

Top EU Brexit lawmaker Guy Verhofstadt is proposing to make a separate Brexit political declaration on future EU-U.K. ties "more binding, more precise."

'Special place in hell'

May will also meet with European Council President Donald Tusk.With the gap between both sides already yawning, Tusk exacerbated the frosty climate on Wednesday by wondering aloud what "special place in hell" might be reserved for those who had no idea of how to deliver Brexit.

Highlighting the sensitivities, a public welcome appearance on camera between May and Tusk was suddenly cancelled, hours before the encounter.

U.K. officials said May's primary concern was not to be "trapped" into a controversial backstop system to avoid lengthy checks on the Irish border which could see Britain linked to the EU in a customs union for an indefinite time.

May will still be looking for changes in the 585-page legally binding withdrawal agreement, something which the 27 other EU leaders continue to vehemently oppose.

May insists that "alternative arrangements" can be found, but EU officials have been waiting for weeks for London to spell out what they are.

Irish Prime Minister Leo Varadkar said Wednesday that a majority in favour of those arrangements probably "only exists because alternative arrangements can mean what you want them to mean."

"Perhaps it's for those who have created these problems to be a bit creative now," he added.

Corbyn calls for customs union

In London, there was some momentum from the Opposition, as the leader of the Labour Party wrote to May spelling out what he wants in exchange for backing the government's Brexit plan.

In the letter, Jeremy Corbyn again demanded permanent British membership in a customs union, which May has repeatedly ruled out.

Corbyn told the prime minister she won't win his backing solely by winning concessions from the EU on the contentious Irish border issue.

The Labour leader said he is seeking "alignment with the union customs code, a common external tariff and an agreement on commercial policy that includes a U.K. say on future EU trade deals."

Corbyn's position is disappointing some Labour Party legislators, who had hoped he would back calls for a second referendum on the Brexit process.