A Eurosceptic Tory minister has been accused of “plain and simple lying” over the possibility of Turkey joining the EU, prompting an extraordinary intervention from the Prime Minister.

Penny Mordaunt, the armed forces minister, said the UK “does not” have a veto over the new membership of states such as Turkey – despite it being a key part of the Treaty of the European Union.

David Cameron said the minister was “absolutely wrong” on the matter, and implied her judgement on other matters should be called into question as a result.

Ms Mordaunt found herself at the centre of the controversy after she endorsed a controversial new Vote Leave campaign poster which shows dirty footprints entering an enlarged British passport with the caption: “Turkey (population 76 million) is joining the EU”.

Asked if she was resorting to “dog whistle” politics, Ms Mordaunt told the BBC’s Andrew Marr Show it was the Remain campaign that was resorting to "scaremongering" and "false reports”:

On Turkey’s chances of joining the EU, she said: “This is our last chance to have a say on this, we’re not going to be consulted on whether those countries should join. Those countries are going to join, it is a matter of when.”

Andrew Marr suggested this was wrong, given “the British government does have a veto on Turkey joining, so we don’t have to let them join”.

But Ms Mordaunt replied: “No, it doesn’t. We are not going to be able to have a say.”

Marr was forced again to bring up the issue at the end of the interview to clarify Ms Morduant’s point. He said: “I’m going to return to this business, because I’m pretty sure that we do have a veto over stopping Turkey joining if we want to. Are you sure that we don’t?

Ms Mordaunt said: “We haven’t… I think that with the current situation, the migrant crisis and other issues in Europe at the moment, we would be unable to stop Turkey joining.

“I think this is a matter for the British people to decide, and the only shot that they will get to express a view on this is in this referendum… I don’t think that the UK will be able to stop Turkey joining.”

Political commentators, Remain campaigners and the Labour party were quick to call out Ms Mordaunt’s claim – but it is the “blue-on-blue” attack from Mr Cameron which threatens to claim a second Eurosceptic cabinet minister in as many months.

The Prime Minister told ITV's Peston on Sunday: "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."

James McGrory, a spokesman for Britain Stronger in Europe, said the minister is "plain and simple lying to people".

"We have a veto on whether Turkey can join the EU," he said. "As does every other EU nation.

"That was disgraceful from Penny Mordaunt on [the Andrew Marr Show]. Criticises dishonesty and then is utterly dishonest about our veto on Turkey."

Labour’s Hillary Benn said Ms Mordaunt was “wrong”, and said Leave “must stop misleading people”.

He said: “Even if – a long time in the future – Turkey did become an EU member, Britain and other EU countries would be able, if they wanted to, to control the movement of workers.”

Thomas Cole, a former foreign policy official with the EU Commission who now campaigns for Remain, said: “Penny Mordaunt just lied on Andew Marr. I should know. I used to work on EU enlargement.”

Faisal Islam, Sky News’ political editor, said the minister’s comments on the programme were “straightforwardly not true”. He reproduced Article 49 of the EU treaty, on countries applying to become a new member of the union, which states: “The applicant shall address its application to the Council, which shall act unanimously.”

And Ben Wallace, one of Ms Mordaunt’s fellow Conservative MPs, said: “What Leave never mention is that accession states, including Turkey, can only join the EU with a unanimous vote of members. The veto applies.”

Elsewhere in the interview on Marr, Ms Mordaunt described the campaign to Remain as an “establishment stitch-up”. Some viewers were quick to point out the irony of such a statement coming from a minister within the Government.

What has the EU ever done for us? Show all 7 1 /7 What has the EU ever done for us? What has the EU ever done for us? 1. It gives you freedom to live, work and retire anywhere in Europe As a member of the EU, UK citizens benefit from freedom of movement across the continent. Considered one of the so-called four pillars of the European Union, this freedom allows all EU citizens to live, work and travel in other member states. What has the EU ever done for us? 2. It sustains millions of jobs A report by the Centre for Economics and Business Research, released in October 2015, suggested 3.1 million British jobs were linked to the UK’s exports to the EU. What has the EU ever done for us? 3. Your holiday is much easier - and safer Freedom to travel is one of the most exercised benefits of EU membership, with Britons having made 31 million visits to the EU in 2014 alone. But a lot of the benefits of being an EU citizen are either taken for granted or go unnoticed. What has the EU ever done for us? 4. It means you're less likely to get ripped off Consumer protection is a key benefit of the EU’s single market, and ensures members of the British public receive equal consumer rights when shopping anywhere in Europe. What has the EU ever done for us? 5. It offers greater protection from terrorists, paedophiles, people traffickers and cyber-crime Another example of a lesser-known advantage of EU membership is the benefit of cross-country coordination and cooperation in the fight against crime. What has the EU ever done for us? 6. Our businesses depend on it According to 71% of all members of the Confederation of British Influence (CBI), and 67 per cent of small and medium-sized enterprises (SMEs), the EU has had an overall positive impact on their business. What has the EU ever done for us? 7. We have greater influence Robin Niblett, Director of think-tank Chatham House, stated in a report published last year: “For a mid-sized country like the UK, which will never again be economically dominant either globally or regionally, and whose diplomatic and military resources are declining in relative terms, being a major player in a strong regional institution can offer a critical lever for international influence.

Tweeting during Ms Mordaunt’s appearance, the official Vote Leave campaign account insisted “you can’t trust David Cameron on Turkey”, and posted a video showing Turkish MPs fighting in Parliament in Ankara.

Vote Leave chief executive Matthew Elliott said: "David Cameron has said he wants to pave the road to Ankara and has repeatedly confirmed it is government policy for Turkey to join the EU.

“The EU is speeding up the process of Turkey joining and we are paying nearly £2 billion to help make it happen. If it isn't on the cards, why are taxpayers footing the bill for it already?