The voting, which happened on Monday, attempted to drive the country out of deadlock after parliament rejected against Prime Minister Theresa May's 585-page EU divorce deal on Friday, marking the deal's third failure in parliament.
The four proposals on Monday sought to avoid a potentially damaging no-deal Brexit before the EU's April 12 deadline, Press TV reported.
The rejected motions considered negotiating a permanent customs union with the EU, a second Brexit referendum, revoking Brexit to avoid a no-deal exit or accepting May's Brexit on the condition of negotiations seeking a new EU customs and single market arrangement.
The failed vote prompted conservative MP Nick Boles, who had proposed the new EU customs and single market arrangement motion, to resign from the party.
"I accept I have failed. I have failed chiefly because my party refuses to compromise. I regret therefore to announce I can no longer sit for this party," he said.
The motions were not legally binding but could have potentially pressured the government to agree to an alternative plan if a strong majority on one of the proposals had been achieved.
Following the vote, Brexit Secretary Steve Barclay suggested that the government may bring the deal for a fourth vote this week to avoid a longer delay to Brexit.
He warned that "the default legal position is the UK will leave the EU in just 11 days time" without a deal.
"Cabinet will meet in the morning to consider the results of tonight's vote and how we should proceed," Barclay said.
Facing the prospect of a no-deal Brexit, European Council President Donald Tusk has called for an emergency meeting on April 10.
On Sunday, European Commission President Jean-Claude Juncker had warned that the EU was “running out” of patience with the UK, urging the British parliament to reach an agreement on a Brexit plan “in the coming hours and days.”