Once upon a time, the BBC banned fascists from its broadcasts. In 1935, when Oswald Mosley’s British Union was near its peak of popularity, organising rallies and marches across the country, the corporation stopped allowing him to appear on its programmes. The ban, unofficially supported by successive Conservative, Labour and coalition governments, lasted 33 years. Its rationale was straightforward: Mosley’s views were too extreme, his supporters too threatening, and his admiration for foreign authoritarians too strong for him to be allowed a prominent place in the national discourse. A line was drawn between what was acceptable and unacceptable in rightwing politics, and Mosley was on the wrong side of it. By the time the prohibition was lifted, in 1968, he was a bitter old man.

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It’s impossible to imagine such a sustained and effective ban on a big far-right figure being imposed in Britain now. Many of our politicians and much of our media have stopped setting, let alone policing, any boundaries between mainstream conservatism and rightwing populism and extremism. The BBC seems reluctant to characterise Donald Trump as a racist. Nigel Farage, despite never having been elected as an MP, has been a panellist on BBC One’s Question Time 33 times. Tommy Robinson has been interviewed on BBC Two’s Newsnight. Meanwhile Boris Johnson, and many of his ministers, party members and newspaper allies, have adopted the boot-boy phrases and demagoguery of the far right. As the home secretary, Priti Patel, told a thrilled Conservative party conference this week: “To the criminals, I simply say this: we are coming after you.” A stronger law-and-order state, she said, “is what the people want”.

Sometimes, the bursting out of rightwing populism from the margins of our politics to its centre happens right in front of our eyes. Recently I went to a protest outside Downing Street against the prorogation of parliament. As the afternoon’s speeches ground on, and children holding remain placards next to proud parents began to look a bit bored, a counter-protest by far-right Brexit supporters, mostly middle-aged men with years of anger in their eyes, gradually built up around us. The police held most of these men back, but not all. Some of them walked among the remainers, shouting “traitors!” in their faces, filming them and asking for their names. At the end of the afternoon, the police advised the remainers to leave together. “Otherwise,” they warned, “we cannot guarantee your safety.” In broad daylight, at the heart of the capital, expressing liberal views in public had been made to feel quite frightening. Mosley would have been proud.

The endless Brexit confrontation has become a perfect environment for nationalists and xenophobes, for people offering short cuts past our stuck democracy. But the origins of this tilt towards the far right lie further in the past: in a calmer, more comfortable period of British politics, when a deep complacency set in.

During the 90s and 00s, the fear of fascism that had hung over British politics through the mid-20th century finally faded to almost nothing. Partly, it was the passage of time: Tory and Labour cabinets, and the electorate, were no longer full of people who had fought Hitler. Yet there was also a change in how politicians thought about extremism. Centrists such as Tony Blair defined themselves very clearly against what they called “the hard left”, and later against Islamic radicalism; they talked much less about the far right.

Many New Labour ministers and thinkers, convinced that politics was becoming milder and less ideological, possibly for good, paid relatively little attention to the fierce rightwing populism that had begun building across Europe. They saw it as a political dead end: part of what Blair belittled as “the forces of conservatism”, which would ultimately be overcome by “the forces of progress”. This disdain towards the populist right was passed on to Blair’s Conservative admirers. In 2006, months after being elected as a liberalising Tory leader, David Cameron described Ukip as “a bunch of fruitcakes and loonies and closet racists”.

‘Sir Walter Walker tried to set up a private army in the turbulent mid-70s.’ Walker in 1955.

Photograph: Keystone/Getty Images

This confidence in moderation was bolstered by an assumption, so widely and strongly held as to rarely need stating, that Britain simply didn’t do fascism. Mosley was just a historical blip, this argument ran; his failure to establish a dictatorship or even a lasting movement, in contrast to the far right’s huge impact elsewhere in 30s Europe, was proof of Britons’ political good sense. Meanwhile, more recent would-be British strongmen were not even footnotes in most histories of modern Britain. Sir Walter Walker was a retired general who tried to set up a private army during the turbulent mid-70s. “The country might choose rule by the gun in preference to anarchy,” he told the London Evening News in July 1974. In 2002, when I included a chapter on him in a book about British Conservatism’s intermittent flirtations with authoritarianism, Jeremy Paxman languidly dismissed my excited discoveries on Radio 4’s Start the Week. Wasn’t I taking the whole Walker episode, he suggested, much too seriously?

Yet during the 00s and 2010s the Blair and Cameron governments began to feed and legitimise some of the far right’s preoccupations: New Labour by using the recklessly loaded phrase “bogus asylum seekers”, the Conservatives by declaring they would drastically cut total immigration. Meanwhile, journalists noticed that the British National party (BNP) was gaining seats in local and European elections. In a more competitive, less deferential media age than the one that accepted the Mosley ban, far-right figures became irresistible invitees for current affairs shows. In 2009, the leader of the BNP, Nick Griffin, appeared on Question Time.

Many people were outraged. Yet to watch the programme now – to see Griffin defensive and flustered, rushing through his crude arguments while under constant attack by the audience, the host David Dimbleby, and the other panellists – is to see a time when rightwing populism was still relatively marginal and under-confident in Britain: not quite media-ready. We live in a different country now.

To marginalise the far right again will be a huge task. In the past few weeks, Britain’s many centrist MPs have finally made a start, by calling out thuggish language, and standing up for parliamentary democracy and the rule of law. And the hard right’s decision to associate itself so closely with Brexit may backfire if Britain actually leaves the EU, and the result is an anticlimax or a disaster. So far, Brexit has been a largely rhetorical project, and rhetoric is the area of politics where ranters and dreamers are most comfortable.

But even if Brexit ultimately damages them and their Tory imitators, they will find other grievances – multiculturalism, non-EU immigration – to keep their movement growing. To avoid aiding them, establishment politicians and journalists may even have to stop giving a voice to far-right figures who exploit confrontations with liberals – in other words, no-platforming, a tactic for which the left is usually condemned. In Mosley’s autobiography, written during the fourth decade of his BBC ban, he complains: “I have been the subject of frequent comment and attack, but … have always been denied the right to reply.” How sweet that frustration sounds now.

• Andy Beckett is a feature writer for the Guardian and author of Promised You a Miracle: Why 1980-82 Made Modern Britain