None of the four alternatives to British Prime Minister Theresa May's Brexit deal receives support from a majority of MPs in the second round of "indicative vote", which kicked off at around 20:00 BST on Monday and whose results were announced at around 22:00 BST.
The process was launched after MPs voted to take control of the Brexit agenda from the government after repeatedly defeating May's deal.
The next most voted option was a plan to stay in a permanent customs union with the EU.
"There is a growing expectation that a (House of) Common's majority could coalesce around a softer Brexit that includes a custom's union but she is facing more threats from cabinet members to resign if she decides to pursue a softer Brexit", MUFG analysts said.
The British cabinet was to gather on Tuesday seeking a way to leave the European Union with a deal in 10 days' time, with torn MPs rejecting every possible path to Brexit.
The impasse has forced May to postpone Britain's original exit day from March 29, but she said it would be "unacceptable" for a further delay beyond European Parliament elections held from May 23 to May 26.
Discount airline easyJet warned Monday that the U.K.'s pending withdrawal from the European Union is causing travellers to hold back on booking tickets amid doubts over what Britain's future relations with the bloc will be.
Conservative MPs have been given a free vote, but cabinet ministers will be told to abstain.
United Kingdom MPs reject Theresa May’s Brexit proposal for a third time
He claimed the establishment of a cross-party government would be in the "national interest" and help resolve the Brexit crisis. The Irish taoiseach Leo Varadkar has been adamant that the European Union will not budge on the issue.
The British cabinet is expected to meet on Tuesday morning to consider how to proceed with the vote outcomes amid speculation about possible resignations, a general election or change of Tory leader.
"I have failed chiefly because my party refuses to compromise", Boles added, announcing that he was quitting the Conservatives to sit as an independent in Parliament.
"For the second half we are seeing softness in both the United Kingdom and Europe, which we believe comes from macroeconomic uncertainty and many unanswered questions surrounding Brexit which are together driving weaker customer demand", easyJet CEO Johan Lundgren said.
Some 25 Labour MPs rebelled against their party whip to vote against the Boles plan, tabled under the banner Common Market 2.0.
Following the result, Guy Verhofstadt, leader of the European Parliament's Brexit committee, said: "A hard Brexit becomes almost inevitable".
"We've got the worst leader of the opposition in the entire history of the Labour party".
The April 12 deadline, imposed by the European Union, gives Britain's politicians less than two weeks to bridge the hostile divide that separates those in her government who want to sever links with the European Union and those who want to keep the ties that have bound Britain to the bloc for nearly 50 years.
He suggested that Wednesday, when MPs may have a third attempt at reaching a majority, was the "last chance to break the deadlock or face the abyss".
The government will make clear its plans for another so-called meaningful vote after Monday evening's Commons vote on different Brexit options.