Update: May's Conservative party came up a few votes shy for a needed majority, making the prospects for a "soft Brexit" all the more likely.   

As Britons headed to the polls on Thursday, it's worth highlighting how the general election could influence the course of that country's exit, or "Brexit," from the European Union--particularly as the race appears to have tightened in recent weeks.

In April, when Prime Minister Theresa May called the snap election, the goal was to shore up more conservative support in Parliament. She insisted that this would put her in a better position to negotiate a successful Brexit: "There should be unity here in Westminster, but instead there is division," May said at the time.

Yet in the weeks leading up to the election, the opposing Labour party has managed to gain an advantage. Opinion polls indicate that the left had closed on the Conservative lead--May's party--thus increasing the possibility of a so-called "soft Brexit," in which the country would negotiate to remain in the single market trade zone. "If you want to keep Britain in the single market, if you want a Britain that is open, tolerant and united, this is your chance," said Tim Farron, leader of the Liberal Democrats, in an April statement. That could benefit many businesses that manufacture abroad, for example, and which could be forced to pay higher tariffs under new trade deals.

By contrast, May has called for what's being dubbed a "hard Brexit," in which the nation would leave the single-market trade zone. While the plan has some backing, it is largely seen as a bust for businesses.

"A lot of companies are going to have a harder time navigating these rules, tariffs are clearly going to be higher, and E.U. countries at the end of the day are the most important partners in trade that the U.K. has," notes Ian Bremmer, the founder and president of consulting firm Eurasia Group, in a previous interview with Inc. "In the near-term, this is going to hurt," he said.

Still, analysts say that entrepreneurs may generally prefer a May victory over a victory for the Labour Party's Jeremy Corbyn, a self-described socialist. In recent weeks, Corbyn has called for increased spending on social and healthcare programs, as well as increasing the corporate tax rate. "Business people find certain aspects of Corbyn's policies disturbing," says Geoffrey Heal, a professor of social enterprise at Columbia Business School.

Meanwhile, the U.K. is reeling from three terrorist attacks in as many months, at a concert hall in Manchester, and at tourist attractions London Bridge and Westminster Bridge. This is liable to affect the election result. Although some have pointed out that the attacks could help May--who is generally perceived to be tough on immigration and security--others suggest that it could hurt her. (May previously served as U.K. home secretary, when austerity budgets limited funding for national police.)

The most recent polling data suggests that Conservatives will still win a majority. May stands to gain some 45 seats in Parliament, which could ultimately strengthen her hand to negotiate a hard-Brexit. Soft or hard, the U.K. is expected to part ways with the E.U. entirely by 2019. The results of Thursday's vote aren't expected in until early Friday morning GMT.