Prime Minister David Cameron on Sunday rejected claims by Vote Leave campaigners that Turkey could join the European Union in the next five years and flood Britain with new migrants.
Vote Leave will launch a poster campaign on Monday showing an open door in the style of an EU passport and the message: "Turkey (population 76 million) is joining the EU. Vote Leave, take back control."
It claims Britain is powerless to stop Turkey joining the EU and enjoying freedom of movement for its citizens.
But Cameron told broadcaster ITV that Turkey's accession was not "remotely on the cards" in the near future and that Britain has a veto over it joining the EU.
Vote Leave is urging voters to support a British exit from the EU, or Brexit, in a referendum set for June 23.
The campaign will also publish an analysis claiming that Turkey will join the EU in the next few years, spurring a wave of migration that would further strain public services and bring Turkish criminals to Britain.
Speaking to the BBC politics on Sunday, Penny Mordaunt, a Eurosceptic armed forces minister from Cameron's Conservative Party, said "with the current situation - the migrant crisis and other issues going on in Europe - we would be unable to stop [Turkey's accession]."
But Cameron rejected Mordaunt's claim, saying that "Britain and every other country in the EU has a veto on another country joining and that is a fact."
"The fact that the Leave campaign are getting things as straightforward as this wrong, I think, should call into question their whole judgement for making the bigger argument about leaving the EU," he said.
During a visit to an Asda supermarket on Sunday, Cameron claimed a Brexit could add about 220 pounds (320 dollars) annually to the average British family's shopping costs.
"Independent studies show that a vote to leave would hit the value of the pound, making imports more expensive and raising prices in the shops," he said.
"Families are better off voting to remain in the EU – the alternative is a leap in the dark that would risk prosperity and security," Cameron said.
Mordant said voting to remain in the EU would "allow people from Albania, Macedonia, Montenegro, Serbia and Turkey to move here freely when they join the EU soon."
"Many of these countries have high crime rates, problems with gangs and terror cells, as well as challenging levels of poverty," she said.