Once a politician calls for the borders to be closed against a single religious minority, he’s going to get called a fascist. The picture editors will find shots of him doing an apparent Hitler salute, there will be front pages in faux German. Which is why no one can blame the Philadelphia Daily News for splashing with a shot of a saluting Donald Trump alongside the headline The New Furor. He deserves it.

And yet name-calling won’t quite cut it. There has to be a better response to Trump, just as those who want to stop Marine Le Pen becoming the president of France need to raise their game. Hillary Clinton, whose default reaction to the Republican frontrunner has so far been laughter, is now “searching for how best to hit back at Mr Trump”, according to the New York Times. So far, says the paper, Democrats have no firm answer, just “befuddlement”.

The problem is the same one posed by Le Pen or any other populist of the right. Demagogues of their ilk, whether the full Trump or the milder, low-tar brand of Nigel Farage, make a pitch that is simple and visceral, and gives both speaker and audience the moral halo of victimhood: our way of life is under threat and no one but me cares about you. They tell a compellingly clear story, in which the truth is obvious, the enemy is plain and the elites are too craven or too stupid to do anything about it. The threat comes from outsiders: foreigners, migrants, refugees or, in Trump’s newly explicit formulation, Muslims.

The reflex response is denunciation, calling the demagogue in question a racist, a bigot or even a fascist. The trouble with that approach is that it doesn’t just denounce the speaker, it denounces those who are listening too. That’s at least 25% of both the US and UK electorates, according to new polls that say that number agree with Trump’s entry ban on Muslims. What’s more, it only serves to vindicate the demagogue’s wider message: “There goes the establishment, closing ranks and trying to shut down a debate it can’t handle.”

The second, more reflective reply offers cool, methodical facts. In the UK, that would mean pointing to the data that shows, say, that migrants actually bring an economic net gain rather than a loss. The centre-left does this a lot, fighting campaign after campaign as if the battleground were in the brain rather than in the gut.

Indeed, next month a new initiative is set to launch “making the fact-based case for Britain to remain in the European Union”. It will be called InFacts. I wish that group well; it will have an important role to play. But it cannot define the wider campaign. Because the political brain is an emotional brain. It responds not to data but to instinct and feeling. A bombardment of statistics rarely wins any political argument: which is partly why Michael Dukakis, Al Gore and John Kerry all lost debates to their less cerebral opponents. Instead, the only way the left can hope to fight a populist fire is with a populist fire of its own.

So what would such a populism of the left look like? Its first move would be not to dismiss, but to understand whatever fear is drawing people to the rightwing flame in the first place – and to show that it understands it.

Donald Trump has Americans currently applauding his repulsive anti-Muslim racism because they are frightened. Some of those cheering will be unreconstructed Islamophobes, of course, but plenty will simply be people freaked out by the reported connection between Islamic State and last week’s shootings in San Bernardino, as well as by the Paris attacks, and worried about their own safety. To win them over, any rejection of Trump has to begin with that fear. Hillary Clinton seems to understand that. “It’s OK, it’s OK to be afraid,” she said this week. “When bad things happen, it does cause anxiety and fear.”

The anti-Farage forces in Britain need to make a similar move on, say, immigration. You can’t keep telling people that their experience is wrong. You have to seem as if you understand their angst, that maybe you even feel it yourself. Sunder Katwala of British Future says that Ed Miliband erred because he tried to tell people that what they were really concerned about when they talked about migration was jobs, housing and wages. “He couldn’t talk about the cultural bit,” about people’s fears at the pace of change in their towns and cities. Instead he left those fears “festering in the subconscious”, waiting to be addressed by Ukip.

Nigel Farage with Tim Aker (right), Ukip’s prospective parliamentry candidate for Thurrock in the 2015 general election. Photograph: Gareth Fuller/PA

Next, any left populism cannot merely nod sympathetically as people describe where they are. It has to meet them part of the way there. It’s often forgotten, but after the murder of Sarah Payne in 2000 the then newly elected mayor of London, Ken Livingstone, suggested whole life sentences and chemical castration for paedophiles. That statement, and others like it, gave Livingstone permission to be more liberal elsewhere. The electorate knew he was not some bleeding heart pushover and so gave him a hearing. The same goes for George Galloway’s recent declaration – and implicit rebuke to Jeremy Corbyn – that if he were confronted with Isis terrorists killing people on the streets of London, he would not merely approve a shoot-to-kill policy, he would grab the gun and shoot the killers himself.

Think of it as a vaccine, a small dose of right-wingery that can inoculate the rest. The exemplar remains the greatest slogan of left populism of recent times: New Labour’s “tough on crime, tough on the causes of crime”. Because you’ve reassured to your right, you’re allowed to go left. The trick is to get the dosing right, and not let the message of reassurance drown out the rest.

Once that’s done, all kinds of paths are open to the left populist. In today’s US, you could appeal to empathy, telling those hailing Trump that their Irish or Italian or Polish great-grandparents were once just like today’s Muslim would-be immigrants to America: decent, faithful people looking for a better life. You could appeal to their better angels, telling them that you know them – and that they’re better than this. Or you could cast Trump as the villain, doing what the rich and powerful have always done – pitting the poor and disadvantaged against each other rather than against the banks, big business and their enablers in Washington, those truly responsible for the pain they’re in. Labour MP Jon Cruddas, who has defeated his share of fascists in his Dagenham constituency, likes to deploy an English version of that message: “Don’t let these people play you for a mug. All they’re doing is pouring petrol on your grievance without offering you a solution.”

The point is, the new populists are on the march. Their rage cannot be fought with statistics. Their canny articulation – and exploitation – of people’s visceral pain cannot be defeated by an appeal to cool reason alone. The blaze has started. It’s time to start fighting fire with fire.