For Conservative prime ministers, trouble tends to come in threes. For Harold Macmillan, the resignation of three Treasury ministers in 1957 sparked the first serious crisis of his premiership, while for Margaret Thatcher, the resignations of Michael Heseltine in 1986, Nigel Lawson in 1989 and Geoffrey Howe in 1990 triggered the end of her government.

Andrew Bridgen, Bill Cash and Nadine Dorries, the trio of serial rebels and virulent Eurosceptics who recently put David Cameron on notice, are not quite in the same category as Heseltine, Lawson and Howe. Yes, they have added to the sense of disarray that surrounds Cameron at present, but the reality has always been that this year will be the Prime Minister’s last in front-line politics unless he can persuade Britain to vote to stay in the European Union on 23 June.

As far as that contest is concerned, the number that should keep pro-Europeans and the Prime Minister awake at night is not three but 18. That’s the number of Albanian migrants who were rescued by the UK coastguard as Cash, Bridgen and Dorries were busy fitting Cameron for his chalk outline. Two British men, both from Kent, were charged with immigration offences, after coastguards rescued them and the 18 Albanians from a small inflatable boat on which they were attempting to cross from France to England.

The same global winds that propelled tens of thousands of people to attempt the treacherous Mediterranean crossing from North Africa and the Middle East last summer are still blowing today. War and disorder in Libya and Syria (both nations that are close to being failed states in all but name), the march of the so-called Islamic State and the ravages of climate change are driving thousands of desperate people to board makeshift boats – some of which would barely be seaworthy in a paddling pool – and attempt to reach a safer nation.

Added to that, the tightening of border controls at Calais and the deteriorating conditions of the camps there make the chance of arriving on the British mainland undetected and without incident an attractive one.

The crisis that hit the shores of Italy and the streets of Turkey will come to the coast of Dover, sooner or later. Some will make it safely to Britain, others will have to be rescued and a few will be caught. But the English Channel is 350 miles long and impossible to police effectively. The prospect of bodies washing up on English beaches this summer is a real one and, regardless, the last days of the referendum campaign will take place against a drumbeat of public fear – some real, some conjured up by the Leave campaign – about a migrant crisis on British shores.

Vote Leave, the cross-party campaign to get Britain out of Europe, had always planned to focus on immigration in the final days before the referendum. It had hoped that this could at least neutralise the Remain camp’s economic advantage but it will now gamble that a laser focus on the people who come to Britain and the money that Britain sends to Brussels will hand it a surprise victory.

Vote Leave will repeat two large and entirely illusory numbers: the £350m that the UK allegedly sends to the European Union every week, and the 75 million Turkish people who are on the brink of being granted access to the single market and thus the unrestricted right to move to Britain.

The reality is that claiming Britain “spends £350m” on its European membership is like claiming that you “spend £10” on a sandwich at Gregg’s: you may hand a tenner over but you get eight quid back. As far as those 75 million Turks are concerned, well: there is more chance of Turkey successfully mounting a manned mission to Mars than of being granted access to the single market any time soon.

But as is all too often the case in politics – the facts are secondary. Last summer, when photographs of Aylan Kurdi, a Syrian boy who had drowned and been washed up on a Turkish beach, appeared on front pages around the world, the reaction in Britain was not a conversation about opening borders or of greater compassion but an increase in support for a Brexit vote. Within the cross-party campaign to keep Britain in the European Union, there is concern that its poll lead would not survive the appearance of yet more bodies on the beaches of the continent.

It certainly would not endure if those 18 Albanians, all of whom remain in detention in Dover, become a sign of things to come in Britain.