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LONDON—The debate over Turkey's place in Europe on Sunday became the latest battle line to be drawn between British Prime Minister David Cameron and campaigners pushing for the U.K. to leave the European Union.

Mr. Cameron responded to claims by Vote Leave, the main group campaigning for the U.K. to leave the EU, that Turkey would soon be allowed to join the EU, giving millions of citizens from the Muslim-majority nation the right to live and work in Britain.

The spat comes weeks before Britons go to the polls, to vote in a referendum on whether to stay or leave the 28-nation bloc.

Advocates on both side of the debate are zeroing in on their strongest arguments, with Leave campaigners highlighting the risks of immigration in the face of warnings by the government-backed Remain camp that the economy will be seriously damaged if the U.K. pulls out of the EU.

On Sunday, Mr. Cameron locked horns with Penny Mordaunt, a pro-Leave proponent who is also a minister in Mr. Cameron's government. The two Conservative politicians gave sharply contrasting accounts of how Britain intends to use its veto over Turkey's possible ascension to the EU.

Ms. Mordaunt said in an interview with the British Broadcasting Corp.'s Andrew Marr that Britain wouldn't be able to stop Turkey joining the EU.

"I do not think that the EU is going to keep Turkey out. I think it is going to join. I think the migrant crisis is pushing it more that way," said Ms. Mordaunt.

Shortly afterward, Mr. Cameron dismissed Ms. Mordaunt's claims in an interview with ITV's Robert Peston.

"On this question of whether or not we have a veto, the Leave campaign are wrong," said Mr. Cameron, "It is not remotely on the cards that Turkey is going to join the EU any time soon. They applied in 1987. At the current rate of progress, they will probably get round to joining in about the year 3000."

With the June 23 referendum only weeks away, Leave and Remain campaigners are hewing to the two issues that will likely decide the vote: immigration and the economy.

Mr. Cameron opened a fresh salvo on this front, too, warning that British households will face higher prices in the event that his compatriots vote to leave next month.

Analysis by the U.K. Treasury suggests post-Brexit uncertainty could precipitate a 10% fall in the value of sterling, driving up the price of imports, Mr. Cameron's office said on Sunday. In turn, this would lead to a family of four paying £ 220 ($319) extra after two years, said Downing Street.

"This isn't about dry economics; this is about the economic security of hardworking families in Britain," said Mr. Cameron in a statement. "Families are better off voting to remain in the EU—the alternative is a leap in the dark that would risk prosperity and security."

Vote Leave were quick to disagree.

"Sterling will not fall if we vote Leave, so claims of prices rises are wrong," said Vote Leave spokesman Robert Oxley in an emailed statement.

Write to Alexis Flynn at alexis.flynn@wsj.com

(END) Dow Jones Newswires

May 22, 2016 21:45 ET (01:45 GMT)

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