Before turning off the TV last night I heard an impassioned spokesman for Save the Children urging David Cameron to do the right thing and accept 3,000 of the unaccompanied children who have come to Europe with papers but no parents. About 26,000 arrived on the continent last year alone.

When I woke up a different Save the Children spokesman was describing the challenging task of feeding 4 million hungry people in vast, drought-stricken Ethiopia. Don’t panic. Hungry Ethiopian subsistence farmers don’t have the money to get themselves to Calais, even if they preferred it to Berlin. Charities seek our money to help them where they live, not our spare room.

That’s Cameron’s policy too. Take a token 20,000 from the refugee camps (plus the kids? Do we do childcare well enough to handle them?), but concentrate most of our financial support in the camps on Syria’s borders and in finding a diplomatic solution to its civil war.

That may require Russian cooperation, which must be why he’s doing his best not to be too upset over Sir Robert Owen’s report on the Alexander Litvinenko murder. He won’t get too much flack from Jeremy Corbyn over that. But the Labour leader, inspecting the Calais “Jungle” at the weekend, thinks he should be taking in more from there too. Cameron’s internal critics think the opposite. Nasty things happen in the ensuing tension.

Tricky, isn’t it? On Radio 4’s Start the Week on Monday someone called the process Darwinian, meaning that only the strongest and fittest, those with the money to pay for the journey north, get to Europe and through the barriers we erect – bureaucratic and barbed wire kinds, the tunnel at Calais too, minor sideshow though it is. Europe can’t take them all, Jeremy. And should it really prioritise the Darwinian survivors?

Either way the crisis is not going to end any time soon, in or out of the EU, or even the Schengen area. After several centuries when Europe exported its surplus population – the people its economic system could not then support – to the rest of the world, the demographic boot is now firmly on the other foot.

No longer economic and militarily dominant as it was between the 17th and 20th centuries, Europe, which had 25% of the world’s population at its imperial peak of 1900, now has about 7%, or 500 million to Africa’s 1 billion and rising fast.

Whereas 20th-century geo-historians such as Fernand Braudel regarded the Sahara, not the Mediterranean, as Europe’s southern border – north Africa was then colonised – Libyans and Moroccans now take them at their word and walk north, just as refugees from war and economic migrants do the same through Greece and Turkey.

As I never tire of saying here, Europe has become what may be the richest undefended empire in history, wholly dependent on American military power – which is also in retreat for a similar mixture of reasons, though less dramatically so.

Europe’s population is ageing and introverted, its political elite has lost its former confidence and, as Costas Lapavitsas writes in Monday’s Guardian, Syriza’s young leaders easily had their bluff called. As Hamish McRae once wittily put it, the EU’s a bit like Bournemouth: elderly and relatively affluent, surrounded by people who are younger and poorer.

Facebook Twitter Pinterest Rightwing protesters hold anti-Merkel posters in Halle, Germany, on Monday. Photograph: Jens Meyer/AP

Left, right and centre, from Cameron to Corbyn, Farron to Farage, almost everyone wants a quiet life, though they can’t agree how best to get there. In any case, if other people are more determined that we don’t get one, it won’t matter what we decide unless we also acquire the will and means to impose our version of events.

That’s what’s going on as Europe, separately and sort-of collectively, struggles to manage the flood of humanity heading towards its south and eastern borders, in both heat and snow. Back in November, just after the Paris massacres, Scots-to-Harvard historian Niall “aren’t I a clever chap” Ferguson wrote an alarming column (£) for the Sunday Times in which he compared the EU’s migration problem with the late and crumbling Roman empire.

Steady on, prof, I thought, as he reminded us all of Edward Gibbon’s version of the barbarian invasion and conquests that culminated in the sack of Rome and what we patronisingly call the Dark Ages. More recent historians, writing as these folk do with contemporary insight, portrayed the collapse as more violent and sudden than Gibbon’s narrative: the result of mass migration from the east coupled with violence. Having acquired Roman knowhow, Visigoths and Vandals set about taking their share.

No, I’m not saying that assorted new arrivals have a blueprint for takeover and a Kalashnikov in their bundles on Cos or Lampedusa, that’s not how things work. But I’ve since grudgingly conceded that Ferguson’s demographic insight and alarm at European disarray are relevant to where we find ourselves. So has Mark Rutte, the Dutch PM, whose turn it is to be EU Council of Ministers chairman this half-year. He too used the late Roman analogy to call for effective border control.

Nicholas Sarkozy, Jean-Claude Juncker, François Hollande and Angela Merkel, the Hercules of the EU, they’re all wringing their hands about border control now, acutely aware that if they have to abandon their Schengen open borders policy – already half gone in practice – then other painfully built features of the EU may rapidly follow.

Good, you may be thinking. But you wouldn’t be thinking it for long. Europe was full of refugees during my early years, we called them DPs, for “displaced persons”, the victims of the second world war and the post-war upheavals. Things settled, western Europe became more integrated and rich under the EU and the American-led Nato nuclear umbrellas.

The fall of the Berlin Wall in 1989 and the extension on those umbrellas to most of the Warsaw Pact states looked like unfinished business, Europe reunited at last, “the end of history” as one clever dick put it at the time. Foolish talk, it did not predict the speed of China’s recovery from 500 years of sloth, the emergence of militant Islam, the near collapse of the western banking system (will we be as lucky in 2016?), Russia’s return, less stable than before, the rise of populist nationalism as the new panacea.

As with much else, Europe’s problem is not that it is too powerful, a threat to sovereignty of member states (all of them, not just us, Nigel), but that it is too weak. It focuses too easily on what it can do rather than what it should do. Hence so many pointless acts of petty interference that alienate the politicians and voters whose goodwill it will need to restore control over borders, asylum and refugees.

I read today that Greece has been given six weeks to stop migrants crossing from Turkey – Ankara is being paid to try harder, but has 1.7 million refugees already – or face the risk of being put into “quarantine” as the EU’s Schengen border is moved to exclude it. The Greeks haven’t done brilliantly but this is a humanitarian crisis on a huge scale, not their fault. They are also grappling with major economic problems, partly of Europe’s making.

Plans emanating from Brussels to share the refugee burden more fairly between member states (ie relieve Greece and Italy) are surely right, as they are to amend the Dublin asylum system that requires applicants to ask for asylum at their first safe point of arrival. The geographical asymmetry of the current crisis wasn’t anticipated 20 years ago, no surprise there either. A properly funded EU border police force would also have helped the Romans manage the Vandals better.

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But will such imperatives all be accepted by members states under pressures of their own. Some are facing an economic squeeze and high unemployment (France), others the rise of rightwing populism right across the cold north (Sweden, as well as Poland) or a public mood that says we’ve already absorbed too many people too quickly (5 million extra residents since 2001 in the case of Britain, and increasingly in Germany, with 1 million in 2015).

All that without even mentioning terrorism or groping. It’s not a happy story and is unlikely to end well. Merkel, Cameron’s best hope for a sellable deal on his EU renegotiation, may be fatally wounded by her generous response to the Syrian surge – generous but politically unwise. Poland’s Donald Tusk says the answer lies in solidarity and global solutions. He’s right, of course, but ...

Failure would be serious because Europe’s own Donald Trumps are waiting in the wings. The Sunday Times has just printed (£) a map of highly fragmented, medieval Europe above a Ferguson-esque analysis that suggests Europe’s post-war message of universal human rights was only possible while “dictator-wardens” in the Soviet bloc and Middle East kept their own people from leaving and heading our way. “Can we have some too, please?”