Michael Gove: Staying in EU 'will add up to 5m to UK population'
Staying in the EU could increase the UK's population by up to 5.23m by 2030, Vote Leave has claimed, putting the NHS under "unsustainable" pressure.
Justice Secretary Michael Gove said the estimates were "robust" and voting to leave the EU would strengthen the NHS.
He argued the National Living Wage was an extra "pull factor" for migrants.
Remain campaigners say the 5m figure is "absurd" as it is based on five states joining the EU by 2020, which they say "is not remotely on the cards".
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Prime Minister David Cameron has said it will be "decades" before Turkey joins the EU and there is no firm date for the accession of Albania, Montenegro, Serbia and Macedonia.
A document from Vote Leave says the EU's commitment to the free movement of people and the UK's new National Living Wage mean net migration from the EU to the UK will be between 170,000 and 430,000 a year - adding between 2.58m and 5.23m people to the UK population by 2030.
The document has moved here.
The group calculates the NHS could have to contend with a new group of patients the size of "four Birminghams", and A&E demand could increase by up to 57%.
Voting to leave could mean "millions of pounds saved in ending EU contributions" could be given to "strengthen" the NHS instead, Mr Gove said.
"Boris Johnson and I will use all our influence with government to give the NHS additional support when we wake up on 24 June. But if we vote to remain, I fear that the NHS will only face additional pressures.
"Even without the accession of any new countries, we can expect a continuing net flow of 172,000 new individuals from the EU into UK every year."
But the EU was committed to allowing five new countries to join, he said, whose citizens would "inevitably" be attracted to the UK: "The idea of asking the NHS to look after a new group of patients equivalent in size to four Birminghams is clearly unsustainable."
The claim: Migration from the European Union will increase the UK's population by between 2.58 million and 5.23 million by 2030. This would create a 28% to 57% increase in demand for A&E services.
Reality Check verdict: Some migration from the EU is expected but the assumptions behind these population forecasts are very unlikely to be realised. An increasing population would put additional demand on A&E but the extent of that increase has not been demonstrated.
The Office for National Statistics predicts that net migration to the UK - from countries across the world, not just the EU - will add up to just under three million by 2029.
Vote Leave says the ONS has "consistently underestimated the true level of migration" in the past and there are "strong reasons to doubt this forecast".
Mr Gove stood by the Vote Leave figures, describing them as "robust and methodologically fair" and denied abandoning the economic argument - which Vote Leave had been focused on at the start of the campaign - to concentrate on immigration.
But the Remain campaign said it was "absurd" to base figures on five new EU states by 2020 and the UK could veto any new country joining, and apply restrictions on free movement for new EU states.
They pointed to comments made by Vote Leave's Boris Johnson to LBC radio in March, when he said Turkey would not join the EU "in the foreseeable future" and the idea of 75 million Turks having visa-free travel was "simply not on the cards".
Foreign Secretary Philip Hammond, who is campaigning the UK to remain in the EU, said: "I think these figures are very often just plucked from thin air and they're not designed to inform - they're designed to confuse."
And former Labour leader Lord Kinnock said: "Wrecking the economy by leaving Europe would make our NHS weaker - and patients would pay the price.
"These figures are nonsense because accession of these countries is not remotely on the cards. But what is certain is that leaving the EU's Single Market of 500 million people would devastate our economy and cut people's wages. Analysis by the Treasury shows it will create a £36 billion black hole in the public finances. This would leave less money available for our health service."
"Patients, doctors and nurses are stronger thanks to our membership of the EU. Leaving would be a leap in the dark that would put our NHS at risk."
Meanwhile European Commission chief Jean-Claude Juncker has told Le Monde that Britain would have to accept being treated like an outsider if it votes to leave the EU.
"Deserters won't be welcomed with open arms," he said.
"That is not a threat, but our relations will no longer be as they are today".
But UKIP Leader Nigel Farage said Mr Juncker's "whole life has been dedicated to building up these false, undemocratic structures in Brussels" adding: "I think Project Fear will now move on to Project Threat."
And Vote Leave's Labour chair Gisela Stuart said: "Another day, another threat from those trying to intimidate the British people into voting to remain in the failing EU - but these extraordinary comments are a new low."