Portsmouth North MP Penny Mordaunt

Penny Mordaunt, also the government’s armed forces minister, has made the claim that Turkey is set to join the EU in the next eight years, and the UK will be unable to block the move.

Ms Mordaunt has also warned of a ‘dangerous expansion’ of the EU and believes countries wanting to sign up have ‘high crime rates and difficult security challenges’ which the EU is not willing to put right.

But Mr Cameron told ITV’s Peston on Sunday: ‘The Leave campaign are making a very misleading claim.’

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Asked if Ms Mordaunt had been wrong to say Britain would not be able to veto its membership, he replied: ‘Absolutely wrong. Let me be clear, Britain and every other country in the European Union 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 should call in to question their whole judgment in making the bigger argument about leaving the EU.’

In a statement to The News, Ms Mordaunt said: ‘Both the remain and leave camps agree on this – accession countries have high crime rates and difficult security challenges.

‘The EU cannot pursue expansionist policies and not give countries the tools to mitigate the security threat.

‘The PM wants these countries in the EU and removed an amendment in the referendum act which would have given the public a say on accession.