European Union flags hang outside the European Commission headquarters in Brussels. Newly re-elected British Prime Minister David Cameron has pledged to hold a referendum on whether the U.K. will leave the EU. Reuters

With his Conservative Party having won a stunning victory in the U.K. elections Thursday, Prime Minister David Cameron will have to follow through on his promise to hold a referendum on whether Britain will leave the European Union. Although Cameron’s campaign promise may have placated citizens who want a Brexit, or British exit, from the EU, there are indications the U.K. ultimately won’t leave.

“I just can’t see how it would pass,” said Jerold Waltman, a professor of political science at Baylor University in Waco, Texas, who teaches a course on British government and politics. “The entire business community will be opposed,” he said.

Among the political opposition, the Labour Party is for ties with the EU, while the anti-immigrant UK Independence Party is against them, but the latter group has little influence (and few votes).

Public-opinion polls show not a majority but a plurality of Britons would like to stay in the EU, with support for it at a five-year high, according to the European Council on Foreign Relations: 45 percent want the U.K. to remain in the EU, while only 35 percent want the country to leave it.

If Britain did leave the EU, the country would no longer enjoy a tariff-free business arrangement with continental Europe. As a result, the costs of U.K. exports to the EU, its largest economic partner, would become more expensive. By most accounts, the U.K. is the third-largest economy in the EU, behind Germany and France.

“I would think that all of the businesses that export products to all of the countries in the EU, they will be affected,” Waltman said. “Britain got into the EU because it didn’t have adequate overseas markets for exports.”

A Brexit could lead to fewer job opportunities for U.K. citizens, some of whom complain that Eastern Europeans from EU nations are taking jobs away from the native-born population.

“There is a lot of anti-immigrant feelings down on the street, and there’s a lot of feeling that the EU overregulates and that Brussels is an unpopular place,” Waltman said. He added that anti-EU Britons may have a change of heart when they realized the economic implications of any exit.

While Cameron has promised to hold a referendum on the U.K.’s status in the EU by 2017, he hasn’t leaned toward one side or the other. He said he will negotiate the terms of the EU treaty, but European Commission President Jean-Claude Juncker said certain provisions, such as citizens’ freedom of movement between EU member states are “non-negotiable,” according to BBC News.

Those negotiations may help form Cameron’s public position, but there’s also the possibility he’ll arrange for the referendum without campaigning for either side. “I don’t know whether Cameron will put any muscle pro or con when it comes to a referendum -- and of course Labor will campaign against it,” Waltman said.