Turkey becoming a member of the EU is not "on the cards" any time soon, UK Chancellor George Osborne has said.
Talks on Turkey's bid for EU integration are being sped up as part of a deal which would see the country help to tackle Europe's migrant crisis.
Tory MP and Leave campaigner Owen Paterson warned that Turkish accession could impact on immigration, and said it was a "real concern" to UK voters.
Mr Osborne told the BBC's Andrew Marr the UK had "a veto" over the issue.
He raised the prospect of the UK stopping Turkey joining the EU unless its economic prosperity was similar to the UK.
Last week, EU and Turkish leaders gathered in Brussels to discuss ways to ease the ongoing migration crisis which is engulfing Europe.
Under the plan - which is not yet finalised - all migrants arriving in Greece from Turkey would be returned. For each Syrian sent back, a Syrian already in Turkey would be resettled in the EU.
In return, Turkey would receive more funding and there would be faster progression on accession talks, including a relaxing of visa restrictions for Turkish citizens travelling to the EU.
On Sunday's Andrew Marr show, Mr Osborne said: "We have a veto over whether Turkey joins or not.
"We can set conditions and we have made it absolutely clear that we will not accept new member states to the European Union and give them unfettered free movement of people unless their economies are much closer in size and prosperity to ours."
He added: "I don't frankly think Turkish accession is on the cards any time soon. We could, if we wanted to, veto it as other countries could."
The idea of Turkey joining the EU is controversial, with critics arguing that a large, mainly Muslim country with many rural poor could change the whole character of the EU.
Conservative former minister Owen Paterson, who is backing an EU exit, told Sky News' Murnaghan programme that the question of Turkish accession was a "massive" issue.
"Letting in 77 million people who have a long 750-mile border with, sadly, incredibly unstable... states, Syria and Iraq, I think is something of real concern to many people."
"This is the lurking huge iceberg under the surface," he added - and predicted it would "undoubtedly" influence the outcome of the UK's in-out referendum on the EU, on 23 June.
Employment minister Priti Patel said it highlighted the "risk" to the UK of staying in the EU. "The only way we can take back control of our borders, economy and country is to Vote Leave," she added.
Boris Johnson has also voiced concerns about the deal, saying he is "very dubious... about having a huge free travel zone".
'Changed his mind'
Meanwhile, speaking to the BBC, Roland Rudd, treasurer of the pro-EU Britain Stronger In Europe campaign, claimed London mayor Boris Johnson - on the Leave side - had wanted Britain to stay in the EU, but changed his mind over the course of a weekend.
Mr Johnson, one of a number of senior Conservatives to have broken ranks from Prime Minister David Cameron to back the Vote Leave campaign, declared his hand last month, after much speculation about which side he would join.
Mr Rudd, who chairs the pro-EU Stronger In campaign, told BBC Radio 5 Live's Pienaar's Politics he was surprised at the mayor's decision.
"Like a lot of people I had conversations with him, pretty recent, and it was absolutely clear he was for in," he told the BBC's Pienaar's Politics.
There was not any shade of doubt at all, he said, and added: "He's clearly changed his mind over a weekend."
Mr Johnson has denied his decision was anything to do with leadership ambitions, saying the UK would be better off outside the EU which "costs us a huge amount of money and subverts our democracy".