The UK would be powerless to prevent Turkey joining the EU despite the "security risks" its membership could bring, a defence minister has said.
Penny Mordaunt said the migrant crisis would hasten talks over Turkey's EU bid and see more criminals entering the UK.
Next month's EU referendum was the "only chance" the UK would have to have its say on the issue, she told the BBC.
David Cameron said the UK had a veto and it would be "literally decades" before Turkey was ready to join.
With just over four weeks to go to the 23 June referendum, NHS boss Simon Stevens said leaving the EU would be damaging for the health service, while the prime minister has said food prices would rise sharply in the event of a vote to leave.
- Follow the latest on BBC Politics Live
- Rival camps step up EU vote claims
- Brexit 'could damage NHS', warns chief
- Reality Check: How soon can Turkey join the EU?
- Will Turkey's EU hopes affect UK vote?
Talks on Turkey joining the EU, which formally began in 1997, have stalled in recent years amid concerns about the pace of economic reform in Turkey, the security situation in the country as well as historical tensions between Turkey and Cyprus.
But Leave campaigners have warned an agreement earlier this year between the EU and Turkey on tackling the migrant flow across the Mediterranean has injected new impetus into its membership bid and it has sought to make the issue a major plank of its argument.
'Dishonesty'
The Leave campaign has warned that if Turkey and six other countries - Serbia, Albania, Bosnia-Herzegovina, Montenegro, Kosovo and Macedonia - who are aspiring EU members were allowed to join, free movement rules within the EU could see many of their citizens seek work in the UK and could lead to a five million increase in the UK's population by 2030.
A million Turks could potentially come to the UK within eight years of joining, they have claimed, a scale of migration that would run the risk of enabling murderers, terrorists and kidnappers to enter the country.
Ms Mordaunt, who is an armed forces minister and leading Leave campaigner, said it was a question of when not if Turkey joined the EU and seemed to suggest the UK's existing power of veto over the accession of new EU member states would not prevent this from happening.
"It's very likely that they will join, in part because of the migrant crisis it's escalating and speeding up. Turkey in particular, but other accession countries coming in," she told the Andrew Marr programme.
Image copyright ReutersWhen questioned by Marr about the UK's veto on accession countries, the Armed Forces Minister replied "Britain doesn't [have a veto]. I do not think that the EU is going to keep Turkey out. I think it is going to join."
Ms Mordaunt complained that it was dishonest "to have a policy of expansion and at same time deny member states what they need to mitigate against it the security risk that comes with it".
"If you are going to pursue an expansion policy, you have to allow us the tools to protect our own interests, to protect our national security. That we do not have," she said.
She added: "This referendum is going to be our last chance to have a say on that. We're not going to be consulted or asked to vote on whether we think those countries or others should join."
'Question of judgement'
Successive British government have been, in principle, in support of Turkey joining the EU if it meets the criteria, a position endorsed by David Cameron several times since he became prime minister. But the mood music has changed in recent months.
Why this issue matters What the leave and remain sides are saying about immigration in the #EUref campaignThe debate
- Total net migration to the UK is running at over 300,000 a year despite the government’s target of cutting it to under 100,000
- Migration from the EU accounts for just under half the total
- EU citizens have the right to live and work in any member state
Leave
- It is impossible to control immigration as a member of the EU
- Public services are under strain because of the number of migrants
- High immigration has driven down wages for British workers
- The official figures underestimate the true level of migration
Remain
- Immigrants, especially those from the EU, pay more in taxes than they take out
- Cameron's EU deal means in-work benefits for new EU migrant workers will be limited for the first four years
- Outside the EU the UK would still have to accept free movement to gain full access to the single market
- Immigration is good for the economy
Mr Cameron said that at the current rate of progress it would be the "year 3000" before Turkey joined. "It would be decades, literally decades, before this had a prospect of happening and even at that stage we'd still be able to say no," he told ITV's Peston on Sunday.
"This is a very misleading claim. Britain and every other country in the EU has a veto on another country joining. That is a fact.
"And the fact that the Leave campaign are getting things as straightforward as this wrong, I think should call into question their whole judgement into making the bigger argument about leaving the EU.
"They're basically saying vote to get out of Europe because of this issue of Turkey that we can't stop joining the EU. That is not true."
The European Commission has said no new countries will be allowed to join until 2019 and, in reality, the process of enlargement will take much longer as countries try to meet the criteria for joining.