(CNN) British Prime Minister Theresa May will meet German Chancellor Angela Merkel and French President Emmanuel Macron on Tuesday, as the UK leader prepares to request another Brexit extension from the European Union.

EU leaders will meet Wednesday to discuss May's request to move the Brexit deadline, which is set for Friday, April 12.

UK lawmakers finally approved a Brexit bill late Monday after weeks of failing to reach agreement on May's proposals or any of the alternative models of leaving the EU.

The bill , which received royal assent and is now law, aims to block a no-deal Brexit, whereby the UK crashes out of the EU without any transition arrangements in place.

Yvette Cooper, the Labour MP who introduced the bill to Parliament, said lawmakers had voted "against the damage (and) chaos that no deal would cause for jobs, manufacturing, medicine supplies, policing (and) security."

However, UK Culture Secretary Jeremy Wright told CNN that no deal "remains a possibility" -- despite Parliament's determination that it should not happen.

He said cross-party talk needed to finish and reach "a sensible conclusion about the best way to leave the EU with a deal."

Those talks -- between May's Conservatives and Labour -- will continue Tuesday, despite the Prime Minister's absence, Downing Street confirmed.

"We are committed to finding a way through in order to ensure we can leave the EU and deliver on the referendum. That will require the parties to work at pace in order to address outstanding issues -- and so ministers and their shadow counterparts will be holding talks (Tuesday)," a spokesman for 10 Downing Street said.

With May seeking another extension, the UK government has started laying groundwork to enable it to participate in European Parliament elections next month , should it still find itself in the EU by the time the vote takes place.

The move signals a possibility that Brexit could be delayed beyond the May 23 election date -- almost three years after Britons voted in a referendum to leave the EU.