The EU faces a "populist uprising" if it fails to take control of the migration crisis, Britain's former MI6 chief has warned.
Sir Richard Dearlove also fears offering visa-free access to millions in Turkey is like the European Union "storing gasoline next to the fire".
The head of the Secret Intelligence Service until 2004, who has previously claimed the impact of leaving the EU on Britain's security would be low, believes the UK referendum will be the "first roll of the dice in a bigger geopolitical game".
His warnings come as key figures on opposing sides of the debate, including David Cameron and Boris Johnson, prepare to deliver a fresh round of speeches to voters as the referendum campaign battle intensifies.
The latest poll by the Daily Telegraph has put the remain campaign in the lead with 51% and the leave camp trailing behind on 45%, a 1% drop since their last poll in April.
The former spymaster said the impact of mass migration is "eating away at the willingness of EU states to act together".
He told the BBC: "If Europe cannot act together to persuade a significant majority of its citizens that it can gain control of its migratory crisis then the EU will find itself at the mercy of a populist uprising, which is already stirring."
He added: "The geopolitical impact is set to reshape Europe's political landscape as those citizens who feel, rationally or not, that their interests and cultural identity are threatened assert their influence."
He argued that while closing the door on migration was not the answer, the EU's offer of visa-free access to 75 million Turks to "stem the flow of migrants across the Aegean seems perverse, like storing gasoline next to the fire one is trying to extinguish".
Visa-free travel to Europe's Schengen area was one of the concessions offered to Ankara in return for Turkey agreeing to take back migrants arriving from its shores into the EU.
Leave campaigner and defence minister Penny Mordaunt said Mr Dearlove's comments confirmed that it was safer for the UK to leave the EU and control its borders.
However, former foreign secretary Jack Straw stressed more recent former chiefs of MI5, MI6 and GCHQ believe the UK is more secure remaining in the European Union.
The Prime Minister will deliver a speech at a World Economic Forum event on Tuesday while former London mayor Mr Johnson will continue his Brexit bus tour.
Ukip leader Nigel Farage, Labour's shadow chancellor John McDonnall and Liberal Democrat Leader Tim Farron will also attempt to win round the public.
Mr McDonnell is expected to criticise Conservative MPs on both sides of the debate for bringing out "the worst in Westminster politics".
The senior Labour MP will use a speech at the TUC in London to promote what he says is the positive case for remaining in Europe.
Meanwhile, Mr Johnson rejected conspiracy claims levelled against Leave campaigners.
He bemoaned the "colossal, glutinous tide of nonsense" from Remain, as the campaigns continued to discredit increasingly frenetic warnings they have issued ahead of next month's referendum.