It may sound like a healthy, bran-based breakfast cereal but Brexit is going to be dominating the national conversation between now and June 23. A moment that's been coming for at least two decades, and maybe much longer, is finally here: Britain will decide its place in the European Union, in or out.

There'll be no Jewish vote to speak of: Jews will divide on the same lines as everyone else, some persuaded by the economic issues, some by security, some by fear of the unknown. There'll be Jews for Out, like the former Conservative party leader Michael Howard, and Jews for In like the Conservative MP and minister, Robert Halfon.

And yet I was not surprised to see that of the JC's panel of six rabbis last week, four were for Remain and not one was for Leave (two were undecided). I suspect that, among those Jews who follow a Jewish gut instinct on this question, their gut will be telling them to stay. And, in this, the legacy of the Second World War will be inescapable.

True, plenty of Outers build their case on the last war. Nigel Farage frequently invokes the 1940 notion of a free Britain standing valiantly against the totalitarian tendencies of the continent. I can see how the supposed threat of a European superstate sends a shiver down Jewish spines especially. Recall the 1990 declaration by Margaret Thatcher's cabinet colleague, Nicholas Ridley, that, "This is all a German racket designed to take over the whole of Europe." Plenty of Jews would have heard that and been ready to vote Out there and then.

But the Brexiteers do not have the monopoly on wartime memories. You can be equally mindful of history and draw the opposite conclusion. You can note the tendency of the peoples of Europe to murder each other in the bloodiest kinds of war over several centuries - the Hundred Years War, the Thirty Years War, the Franco-Prussian War, two world wars in the last century - and conclude that this is what, unchecked, Europe's nations do to each other.

And yet for the past 60 or so years, the major nations of Europe have not fought each other. Those within what is now the European Union have instead traded together, in peace and prosperity. Some might say that's a coincidence, that even without the EU, Germany and France would not possibly have taken up arms against each other. But surely the more rational view is that the existence of the EU can claim some credit for this outbreak of relative tranquillity. Disputes that would once have been settled by lethal combat have instead been resolved through all-night meetings in Brussels. I know which I'd prefer.

Jews have a mortal interest in all this. War in Europe brings desperate suffering to everyone, of course, but it has inflicted a very particular pain on Jews. For all its huge flaws – and the EU is a clunky, often dysfunctional entity currently tested to its very limits by migration and the strains of a single currency - the notion of cohering Europe's nations into a single market rather than having them fighting each other to the death has been a good thing. Maybe even a life-saver.

With a dangerous, toxic populism on the rise on both sides of the Atlantic, and with an anti-immigration, anti-outsider mood spreading, Jews would surely want to strengthen, not weaken, an organisation that demands democracy and respect for the human rights of its members - one that prefers tedious jaw-jaw to murderous war-war. For that reason, I hope - and, actually, I expect - that, come June 23, most British Jews will vote to stay in.

Jonathan Freedland is a columnist for the Guardian