British lawmakers on Monday voted in favor of an amendment which would lead to a series of indicative votes on Wednesday on "alternative ways forward" on Brexit.
MPs voted 329 to 302 for the amendment tabled by Oliver Letwin.
The vote came after British Prime Minister Theresa May vowed the government would oppose the amendment.
May said she was "sceptical" about the process of indicative votes and would not commit to delivering the outcome of the votes.
Shortly before the vote, Richard Harrington resigned as business minister, saying he will vote in favor of the Letwin amendment.
Jeremy Corbyn, the leader of the Opposition Labor, had called his party to vote for the amendment, slamming the government's approach to Brexit as a "national embarrassment. "
The latest development came after May admitted that there is "still not sufficient support" in the House of Commons for a third "Meaningful Vote" on her Brexit deal.