If statistics won political arguments, the nation would be more riled by tax avoidance than benefit fraud, which they would know is a tiny problem; they’d be convinced that only a tiny proportion of teenagers become pregnant; and they’d realise that crime has long been falling, not rising.

Today’s study on immigration from University College, London should, of course, be welcomed by all of us who refute the pernicious idea fanned by cynical media outlets and politicians that Johnny Foreigner is responsible for our country’s myriad problems. Rather than representing a drain on Britain’s hard-pressed finances, European migrants made a net contribution of £20bn to the exchequer between 2000 and 2011. They are, essentially, walking, talking deficit reducers. But try responding to someone’s expressed hostility towards immigration with “Did you know that a study reveals immigrants have contributed £20bn to the nation’s finances in the first decade of this century?” and see where it leaves you.

Take benefit fraud. The default view is that it is rampant: last year, polling suggested that the average Brit thought 27% of social security spending is claimed fraudulently. Try telling someone that the real figure is just 0.7% until you turn purple: more often than not, they will point out local examples of individual benefit fraudsters. Anecdotes end up trumping statistics. But is this any surprise? We are human beings, and emotional creatures at that: not calculating androids. When tabloids hunt down the most shameless, widescreen TV-addicted so-called “benefit scrounger” and splash their lives in the most tawdry fashion across front pages, they know that human stories resonate with their readers, and that their blood will boil. In any case, we all tend to be more convinced and engaged by facts that confirm our worldview than those that do not.

It gets even trickier than that, too. Earlier this year, Nigel Farage was confronted with figures demonstrating that immigrants did indeed pay their way. His response? “There are some things that matter more than money.” If, he added, the arrival of another 5 million to British shores left us “all slightly richer”, he would rather that we were not slightly richer. It was ingenious trolling of the pro-immigration left, painting them as money-obsessed neoliberals, while he was the champion of community and people (well, non-immigrant people, anyway).

As the political linguist George Lakoff puts it, the right get all this far better than the left. “Conservatives understand that communication has to do with the moral basis,” he argues. Using statistics can be useful within reason, but in his view, only if they comfortably sit with a broader frame of argument.

On the other hand, those that believe the Ukip tide can only be driven back by anti-immigration bashing are themselves stubbornly arguing with reality – and should listen carefully to the likes of Lakoff. Both Labour and the Tories have repudiated past immigration levels, and promise numerous crackdowns: it has only served to shift the political debate on to terms most favourable to Ukip. The party has thrived during the great anti-immigration auction of modern politics: they will always be the most trusted to crack down most effectively on immigration. Labour and Tory promises simply fuel widespread cynicism about the two main parties: voters point to a mismatch between what is promised and what is delivered. In any case, it’s often communities with little immigration – but many social problems – that are convinced by anti-immigration mantra. Londoners, after all, have not been seduced by Farage’s purple army.

So how do those of who resist the anti-immigration pandemic win? We surely need to talk far more about stories: like our own personal experiences, or those of relatives being cared for by Lithuanian nurses or Nigerian careworkers. But we have to shift the debate, too. Our economy was trashed by a financial elite. Wealthy tax-dodgers refuse to cough up even as public services are slashed, while the average Brit has to pay every penny the taxman expects. Greedy employers leave millions of British workers in poverty. There aren’t enough council houses because politicians haven’t built them; the secure jobs aren’t there because governments have allowed them to be stripped from the economy.

These are the real villains responsible for the multiple disasters affecting Britain, not immigrants, and surely where anger has to be refocused. Easy to pull off? No. But it at least it has a chance of success. Using statistics to change people’s minds, on the other hand, is surely doomed to fail.