David Cameron refused three times to say he would veto Turkey's entry into the European Union last night as he faced public anger over his failure to curb immigration.

Appearing on a special Question Time, the Prime Minister repeatedly ducked the question, claiming there was no prospect of the country becoming a member in the near future.

He claimed the issue was 'the biggest red herring in this referendum debate' and that voting to leave for fear of Turkish entry would be a 'crazy thing to do'. But given three clear opportunities to say he would use his veto to stop it, he declined to do so.

Vexed: David Cameron points his finger as he is taken to task on a BBC Question Time special last night

Appearing in his final TV debate before Thursday's vote, Mr Cameron received a mauling from the audience on his Government's approach to tackling EU immigration. He also risked accusations he was patronising the public after he said people have been finding the debate 'perhaps quite confusing'. He added he needed to do 'better' in getting the Government's message across.

The debate also saw host David Dimbleby shock the audience after mistakenly saying the first question came from an audience member called 'Jo Cox'. He immediately apologised for the 'terrible' gaffe' and called the correct audience member, who asked Mr Cameron about the murdered MP.

The issue of Turkey's accession has been a highly charged one, with the Leave camp claiming free movement rules could give millions of Turkish citizens the right to work in Britain.

'Terrible gaffe': The debate also saw host David Dimbleby, pictured with the Prime Minister, shock the audience after mistakenly saying the first question came from an audience member called 'Jo Cox'

Last night Brexit campaigners said Mr Cameron sidestepped the question because he is actually a strong backer of Turkish membership. As recently as two years ago, he said: 'In terms of Turkish membership of the EU, I very much support that.' Vote Leave chief executive Matthew Elliott said: 'You cannot trust Cameron on Turkey.'

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During the debate in Milton Keynes, audience member Michael Tindale asked Mr Cameron: 'Will you veto the accession of Turkey into the EU?'

The Prime Minister replied: 'I don't think it's going to happen for decades, so as far as I'm concerned the question doesn't arise.

'I think this is the biggest red herring in this whole referendum debate. I can't find a single expert anywhere in the country or in Europe who thinks that Turkey's going to join the EU in the next three decades.

'This issue doesn't arise and I feel strongly about this because people are getting through their letterbox leaflets from Leave saying basically Turkey's gong to join the EU – not true; there's going to be a European army with Britain in it – not true; and we give £350million a week to Brussels – not true. If we want to vote to leave ... let's not do it on the basis of three things that are completely untrue.'

Asked by Mr Dimbleby if he would veto Turkey's entry, Mr Cameron replied 'It's not going to come up', prompting jeers from the audience.

'If this was going to happen in the next couple of years I would not support it, but it's not,' he said. He added that voting to Leave and 'damage our economy' on the basis of Turkey joining would be 'a crazy thing to do'.

When asked again by Mr Dimbleby why he will not say he will veto Turkish entry in the future, the Prime Minister again sidestepped the question. He said Britain was being 'positive' to Turkey because we want it to be a 'Western-leaning' country, but admitted it 'isn't going very well at the moment'.

Last night Mr Elliott said Mr Cameron had refused to say he would veto Turkey joining 'because – in his own words – he is the 'strongest possible advocate' of Turkey joining. He has said before that he is 'angry' that it is taking too long for Turkey to join.

'The EU has recently accelerated talks with Turkey with David Cameron's support and UK taxpayers are sending £1billion ... to help them join.'

Voters who challenged Cameron on migration

'You say that your policy that you've negotiated with Europe cannot be overruled – it can. So are you really a 21st-century Neville Chamberlain waving a piece of paper in the air, saying to the public this is what I have, I have this promise where a dictatorship in Europe can overrule it. Simple answer – yes or no?'

Left: 'I think it's only logical – if we have absolutely no limitations on immigration from the EU, people are obviously going to emigrate over here. We've got a public sector [and] our NHS under tremendous strain. You're not doing anything to invest in them to make them stronger or better, [while] knowing full well that if we don't put a limit on this immigration – and the only way to do that is to leave the single market – then everything is just going to get flooded. You're not doing anything to counter-balance all the immigration coming in to these services.'

Right: 'You say that your policy that you've negotiated with Europe cannot be overruled – it can. So are you really a 21st-century Neville Chamberlain waving a piece of paper in the air, saying to the public this is what I have, I have this promise where a dictatorship in Europe can overrule it. Simple answer – yes or no?'

Above: ‘You said Europe is increasing work-wise. Spain, Greece, Italy, France have got higher unemployment than we have and no prospect of increasing jobs. Why are you telling us that Europe is increasing [jobs] when it is not? Europeans come here because they see the problem at home and yet we try and stay in Europe and not see the problems that they have got. You want to spend five minutes with me – I can tell you all about it.’