LONDON, March 11 (Xinhua) -- British Prime Minister Theresa May on Monday secured "legally binding" changes to her Brexit deal just less than 24 hours before a meaningful vote in the parliament on the deal, according to senior British official here.

David Lidington, the British Cabinet Office minister, told the House of Commons that the parliament will vote on this "improved" deal on Tuesday.

The changes "strengthen and improve" the withdrawal agreement that will see the UK leave the EU, as well as its future relationship with the bloc, said Lidington, who is the prime minister's de facto deputy.

May, who is fighting to save her Brexit deal with the European Union (EU), arrived in Strasbourg late Monday for last-ditch talks with senior EU officials in order to have the withdrawal agreement passed in the parliament.

"The EU cannot try to trap the UK in the backstop indefinitely, and that doing so would be explicit breach of the legally binding commitments that both sides agreed," Lidington said.

The European Commission earlier voiced its hope that the members of parliament will back the UK-EU agreement, adding that it is up to them to decide what the country will do in next step on Brexit.

The UK is due to leave the EU on March 29, but MPs rejected May's withdrawal deal by a large margin in January and demanded major changes. Before her Monday trip to the European continent, May has failed to secure significant concessions from Brussels.

If May's deal is voted down on Tuesday in the parliament, she then faces a possible defeat on a second vote on Wednesday to prevent a no-deal Brexit on March 29, and a third vote on Thursday to extend the Article 50 divorce process -- likely until the end of June.