Britain's Prime Minister Theresa May leaves the House of Commons on April 1, 2019 in London, England. Chris J Ratcliffe | Getty Images News | Getty Images

Drastic measures surrounding Brexit — including a no-deal departure or a snap general election — could be on the cards after the British Parliament failed yet again to agree on any alternative options. Having rejected Prime Minister Theresa May's Brexit deal three times, U.K. Members of Parliament (MPs) voted Monday evening on four alternative options in the process, but all of them were rejected by a majority of lawmakers. The option that came the closest to gaining a majority was a proposal to keep Britain in a permanent customs union with the EU. Meanwhile, a proposal for a confirmatory referendum on any deal got the most votes but was defeated by 292 to 280. There is an increasing expectation now that Britain could go in one of four directions — toward a no-deal departure from the bloc, holding a snap general election, Parliament agreeing to the U.K. remaining within a customs union with the EU and/or holding a confirmatory referendum on any eventual strategy.

No deal or a fourth vote?

The defeat of alternative proposals has thrown British politics and Brexit into further confusion just days ahead of a default "no-deal" departure from the EU. There is also a tangible sense of disbelief in Europe at the inability of the U.K. to agree on Brexit. Speaking in Brussels Tuesday, the bloc's chief negotiator Michel Barnier said a no-deal departure was becoming more likely "by the day," and that a strong justification would be needed for the EU to agree to a longer Brexit delay.

Brexit Secretary Stephen Barclay reminded Parliament Monday night that Britain was scheduled to leave the EU on April 12 if no deal was in place. A no-deal exit is seen as a dreaded cliff-edge scenario for businesses where the country has the rely on WTO trading rules. But another delay to the departure date may need to be lengthy with the U.K. being urged to participate in EU Parliamentary elections in late May. A lengthy delay is a concern for pro-Brexit politicians who worry that it could lead to the whole process losing momentum. Prime Minister May could attempt to hold a fourth vote on her Brexit deal later this week, despite three earlier defeats of the withdrawal agreement. Meanwhile, opposition Labour party leader Jeremy Corbyn called for another round of so-called "indicative votes" for Wednesday. Sterling fell almost 1 percent to $1.3048 following the votes Monday night and was trading around the same mark Tuesday morning; London's FTSE 100 index was 0.3 percent higher in early deals. Steen Jakobson, chief investment officer at Saxobank, told CNBC Tuesday that parliamentary debates over Brexit resembled a "trench war." "If we go to the market implication, the hard no-deal (Brexit) has to be priced higher and higher for every hour that passes without any decision."

Customs union or an election?

As Parliament shows itself so far unwilling to find a compromise, Brexit watchers have spoken of the possibility of a snap general election. How that could turn out is anyone's guess with Brexit throwing up unprecedented division among lawmakers and the public. J.P. Morgan Economist Malcolm Barr noted that "the next day or so is likely to involve no small amount of finger pointing among those seeking either a 'softer' Brexit or a 'People's vote'." A People's Vote refers to a referendum on the Brexit deal on offer or revoking the whole departure process. "We continue to think that a general election is the single most likely path forward in the coming weeks, even though that event raises a lot of questions for politicians on all sides," Barr said in a note Monday evening. "With the indicative votes process having come so close to identifying a 'softer' path tonight, it looks likely more bargaining and tweaks to the motions will generate a positive outturn on Wednesday. It is not clear to us how PM May can forestall that, and the potential split in her party that could follow."