LONDON—Britain headed to the polls Thursday to cast votes in a hotly contested election that will likely determine the country’s strategy for exiting the European Union, after a campaign colored by three terrorist attacks in as many months.

Polling day marks the end of a short, tumultuous campaign, which initially focused on the coming Brexit negotiations but quickly shifted to other concerns, including health and social care, before being disrupted in its final weeks by attacks in Manchester and London.

Opinion polls suggest Prime Minister Theresa May, who leads the center-right Conservative Party, will fend off socialist veteran Jeremy Corbyn, leader of the main opposition Labour Party.

But surveys show that the government’s advantage has shrunk over the course of the six-week campaign. It now stands at between 1 and 12 percentage points, depending on the pollster, down from 20 points or more at the start of the campaign.

The U.K.’s “first-past-the-post” electoral system, in which only the candidate with the largest number of votes in a given constituency gets elected, means that Britons could wake up Friday to a wide range of scenarios.

Depending on which opinion polls are right, the vote could return a strengthened Conservative government, or one whose majority will be similar to the current slim margin of 17 lawmakers. A minority of polls suggests the ruling party could even lose enough seats to allow the Labour Party to form a minority or coalition government.

The recent sharp reduction in the Conservatives’ lead, poor past reliability of voters’ surveys and uncertainty about turnout rates all conspire to “make this election tricky to call,” said Kallum Pickering, senior U.K. economist at Berenberg Bank in London. He put the probability of the Conservatives winning an increased majority—the most likely scenario according to his projection—at 35%.

The Conservatives look likely to pick up a majority of the nearly 4 million votes—12.6% of the total—cast for the anti-EU UK Independence Party in the 2015 election. UKIP’s support has shrunk since last year’s Brexit referendum and now stands at about 4%. A recent survey by Opinium Research LLP showed that 49% of past UKIP voters are now supporting the Conservatives, with only 13% switching to Labour.

Mrs. May called the snap election in April, seeking to strengthen her party’s thin parliamentary majority ahead of the Brexit talks, which formally began in March and are due to last at least two years.

The campaign’s initial focus on Brexit was seen to likely favor the incumbent. Mrs. May, who had campaigned for the U.K. to remain in the EU, has laid out plans for a clean break with the bloc, which would see it leave the European single market to gain tighter control of immigration, an important issue for many British voters.

She offered what she repeatedly described as “strong and stable” leadership in contrast to what she depicted as “chaos and confusion” under Mr. Corbyn.

Mr. Corbyn’s Labour Party said it would prioritize retaining the benefits of the single market and maintaining closer links to the EU, hinting at a softer approach to the talks. But with the party’s loyalty split between young, urban voters, who largely backed remaining in the bloc, and voters in Labour’s traditional working-class strongholds, who overwhelmingly favored Brexit, the party struggled to challenge Mrs. May on the issue.

It had more success in reaching wavering voters weary of years of Conservative belt-tightening with a populist platform that included nationalizing railways, free child care and free college tuition. These pledges—and the contrast between Mr. Corbyn’s relaxed campaigning style and Mrs. May’s stiff appearances on the stump—helped Labour narrow the gap in opinion polls during the six-week race.

As terrorism came to the fore in the campaign, the Conservatives, generally regarded as the law-and-order party, didn’t seem to gain. While Mr. Corbyn’s past links to members of the Irish Republican Army and hard-line Islamic groups were criticized, Labour emphasized the cuts in police numbers while Mrs. May was Home Secretary and responsible for policing from 2010 to 2016.

Pollsters say the significant discrepancies between their projections stem from varying assumptions on turnout, which might prove critical to the result. Both parties could face a significant challenge in getting their supporters out to one of the 41,000 polling stations. Conservative voters could see the election as a foregone conclusion and not bother to vote. The Labour Party enjoys strong backing among under 25-year-olds, a group that is traditionally the least likely to vote.