LONDON — When Britons vote on their nation’s future with the European Union on June 23, they’ll also likely determine the political future of British Prime Minister David Cameron and his flamboyant rival, Boris Johnson.

Cameron, who is campaigning to remain in the 28-nation bloc, is going head to head with the former London mayor, who is leading the campaign for a British exit — “Brexit.” Cameron argues that remaining a member brings economic, political and security benefits to the United Kingdom. Johnson says the EU tramples on British sovereignty over issues such as immigration and business regulation.

Cameron “would find it very difficult” to remain in office if Britain votes to leave the EU, said Quentin Peel, an associate fellow in the Europe Program at the Chatham Housethink tank. “He’d certainly be forced to resign quite quickly,” Peel said. “I really don’t see how long he can last.”

Mark Stuart, an assistant professor at the University of Nottingham’s school of politics and international relations, said Cameron “would have no other option than to resign as leader of the Conservative Party” if the Brexit camp prevails.

“Having staked all his political reputation on staying in the U.K. and pre-announced his retirement date, all Cameron’s political capital would be gone,” Stuart said. Cameron has said he will not lead the Conservative Party after the next election in 2020, but will run as a member of Parliament.

Cameron promised during last year’s parliamentary elections to hold a referendum on Britain’s continued membership in the EU. This year, he negotiated concessions from the bloc to give the U.K. more say on economic, social and defense issues affecting the country.

Cameron and Nigel Farage, leader of the anti-EU, anti-immigration U.K. Independence Party (UKIP), took part in an ITV debate Tuesday night.

“No deal is better than the rotten deal that we have at the moment,” Farage said.

Cameron urged Britons not to take Farage’s “Little England option.”

“He is so keen to get us out of Europe that he is prepared to sacrifice jobs and growth along the way,” Cameron said of the UKIP leader.

Matthew Goodwin, a professor of politics and international relations at the University of Kent, said Cameron’s successor in the event of Brexit “would almost certainly be an openly Euroskeptic Conservative MP.”

Many consider Johnson to be that Conservative Party Euroskeptic.

“If Brexit wins, then it appears likely that Boris Johnson, who is extremely popular among Conservative rank-and-file members, will replace David Cameron,” Goodwin said.

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Peel said Johnson’s lead role in campaigning for a Brexit could work against him. “I think there will be an effort to elect somebody who can unite the party rather than someone who’s taken one end of the debate,” he said. “What we’re seeing is one of the bloodiest civil wars in any political party for a long time.”

Finding a candidate to unite the party won’t be easy, considering how bitterly divided Conservatives are on the issue.

Former Conservative prime minister John Major, who wants to remain in the EU, launched a blistering attack on the Brexit campaign last Sunday, a stark reminder of the party’s split. Major described Johnson as a “court jester” during an interview on the BBC’s Andrew Marr Show.

“I think I would offer him this piece of advice — if the leave campaign led by Boris continues to divide the Conservative party as they are doing at the present time, and if Boris has the laudable ambition, for it is a laudable ambition, to become prime minister, he will find if he achieves that he will not have the loyalty of the party he divided,” Major said.

The latest poll by market research YouGov and the Times published Tuesday said 43% of the respondents planned to vote to remain, 42% would vote to leave, and 11% didn’t know.

Henry Hutchins, 67, chief executive of a real estate company in Plymouth, southwestern England, said Cameron will “have to go” if the nation votes for Brexit.

“He’ll have lost too much face, he’s not handled the campaign properly, and I think he and the chancellor (Finance Minister George Osborne) will both go,” said Hutchins, who favors Brexit.

“Boris Johnson I have half a sneaking suspicion he’s using Brexit as a way of putting himself in a position to take over.”

Bill Hart-French, 60, a photographer from London, said he thinks Cameron will go regardless of the outcome of the referendum because of the Conservatives’ rift.

“I don’t think some of these wounds will heal,” he said.

“I did think Boris Johnson could be the next prime minister — as a Londoner we know that he was a very effective politician (as mayor). I think he’s been too cartoonish during this campaign. I think he’s seen less seriously by the public.”