European Commission President Jean-Claude Juncker has hailed the new Brexit deal amendments he agreed with British Prime Minister Theresa May but has warned the UK that it won’t be getting “a third chance”.

Speaking at a late-night news conference at the European Parliament building in Strasbourg on Monday, Juncker and May announced changes to the Brexit deal designed to assuage the concerns of the British Parliament, which is to vote again on the UK’s withdrawal agreement on Tuesday.

The original Brexit deal was killed by the British Parliament in January by a margin of 230 votes, the worst parliamentary defeat in British history.

The most important change in the newly announced amendments of the EU – UK Brexit deal refers to the highly contentious Northern Ireland backstop deal: granting Britain the right to start a “formal dispute” against the EU if the Union tried to keep the UK tied to it indefinitely using the Northern Irish backstop.

During his joint address with May, EC chief Juncker warned the British MPs they would be putting everything at risk if they voted down the deal on Tuesday.

“In politics sometimes you get a second chance. It is what we do with that second chance that counts. There will be no third chance,” the EU leader declared.

“Let us speak crystal clear about the choice – it is this deal or Brexit might not happen at all,” he warned.

Juncker and May agreed on two new documents to amend the already existing Brexit deal that got struck down by the British Parliament in January: a “joint legally binding instrument” on the withdrawal agreement, and a “joint statement” adding to the political declaration (the statement in the deal about the UK and EU’s future relationship).

“Our agreement provides meaningful clarifications & legal guarantees to the Withdrawal Agreement & backstop,” Juncker said later in a tweet.

“The choice is clear: it is this deal, or Brexit may not happen at all. Let’s bring the UK’s withdrawal to an orderly end. We owe it to history,” he urged.

The “second chance”, in Juncker’s wording, secured by British Prime Minister May from the EU with respect to the Brexit deal was quickly criticized by her critics as insufficient.

British opposition Labor Party’s leader Jeremy Corbyn was swift to call upon the Labor MPs to vote against the amend Brexit deal on Tuesday.

“Since her Brexit deal was so overwhelmingly rejected, the prime minister has recklessly run down the clock, failed to effectively negotiate with the EU and refused to find common ground for a deal Parliament could support,” he added.

“These publications need careful analysis. We will be taking appropriate advice, scrutinising the text line by line and forming our own judgement,” said a spokesman for the Democratic Unionist Party of Northern Ireland, the coalition partner of May’s ruling Conservatives, which has been adamantly opposed to the Brexit deal and especially the Northern Irish backstop.

If the British Parliament rejects May’s Brexit deal once again in the Tuesday vote, it is expected to vote on Wednesday of whether the UK should leave the EU without a deal.

If it goes for the no-deal option, on Thursday, the British Parliament could vote on whether to ask the EU for a delay to Brexit.

(Banner image: European Commission on Twitter)