Not for the first time, the UK is in the grip of a backlash against equality and diversity. Already disadvantaged parts of the population are having the existence of that disadvantage denied – and the limited legal redress for it, which has been won over decades, such as the 2010 Equality Act, threatened with repeal. Two of the largest political parties, much of the media, street protesters, online activists, opportunistic rioters and organised fascists are all working to erase aspects of British multiculturalism, by lawful means and otherwise. In the decade since the Brexit referendum – which awoke semi-dormant forces of social conservatism and nationalism – this reactionary campaign has gained more and more momentum.

Its targets have widened and solidified: from “wokeness”, multiracial cities, diversity, and equity and inclusion policies to immigrant cultures of all kinds, so-called two-tier policing and the general conduct of local and central government. “Britain is a two-tier state – against white people,” claimed Nigel Farage in a sweeping Reform UK policy statement on Sunday. “Anti-whiteness is institutionalised into every aspect of public life.” His party, still consistently ahead in the polls, promises to work relentlessly against this supposed injustice when it takes office, copying the confrontational and divisive tactics of Donald Trump.

Meanwhile the Conservatives, under the ever more rightwing and Reform-influenced leadership of Kemi Badenoch, pledge to get rid of a key part of the Equality Act, the public sector equality duty. It requires state institutions to “have due regard to the need to eliminate discrimination, harassment [and] victimisation … advance equality of opportunity … [and] foster good relations” between disadvantaged and non-disadvantaged Britons.

Between 2010 and 2024, five successive Tory governments saw no need even to amend this consensual Labour legislation. Yet last week Badenoch said it must be repealed, as “part of our plan to remove identity politics entirely from the public sector”. Switching to the more respectful tone with which she addresses businesses, she continued: “Hopefully the private sector will follow suit, because they have this problem too.”

Only a minority of Britons are actually enthusiasts for this backlash. A survey published this week found that 17% “strongly agree” that “the growth in the Muslim population poses a foundational threat to UK culture” – one of the main preoccupations of campaigners against multiculturalism. “Tracing changes in values across a 30-year period,” wrote the political scientists Laura Serra and Maria Grasso last year, “we find that … [UK] sociocultural values have been consistently shifting towards social liberalism – a change that is driven primarily by generational replacement.” The conservative older Britons upon whom the backlash and its associated political parties and movements still heavily rely, for all the online and street visibility of younger reactionaries, are gradually dying out.

Yet as has been shown regularly since Brexit, angry rightwing minorities, amplified by rightwing papers and digital media, sometimes encouraged and funded by rich allies in America, can easily dominate British political discourse. Meanwhile, the less politicised or more liberal majority either tunes out, pushes back too little, or gives ground.

For much of Keir Starmer’s leadership, Labour has surrounded itself with Union flags, produced ever tougher immigration policies and treated many of the grievances driving the backlash as “legitimate” – even those based on fears and ignorance rather than social realities, such as the widespread conviction that immigration is surging, when it has actually fallen fast over the past year. Occasionally, Starmer has spoken up for “our beautiful, tolerant, diverse country”, and against those who “just want to stir the pot of division”, as he put it at Labour’s conference last year. But this strategy of intermittent challenge and more general appeasement has failed: Labour remains loathed by most socially conservative voters and has been abandoned by many liberals, while the backlash parties have radicalised further and the potential victims of their policies have grown more scared.

How might Labour and other political forces that support equality and diversity deal better with the backlash? Sadiq Khan’s London mayoralty suggests one approach. Like Starmer, he is no great orator, but he has been re-elected twice during a period of general Labour unpopularity – partly because he has refused to allow the right to define the legitimate makeup of London, instead always presenting the city’s diversity as its strength. At last month’s local elections, the already low Tory vote in London fell, while Reform performed much worse than elsewhere.

Yet today’s multiracial, sexually tolerant capital, which until the May elections had been dominated by Labour for 30 years, and which is now also a stronghold of Zack Polanski’s socially liberal Greens, is a relatively easy place for a Labour politician to fight a socially conservative backlash. It was a lot harder back in the 1980s, when the city was much less diverse and Margaret Thatcher’s illiberal Conservatives were often its most popular party. Then as now, rightwingers in parliament and the media were aggressively seeking a return to “traditional values” after the liberal advances of the 1960s and 1970s. The far right was active against immigrants on the streets, and much of Britain appeared to be moving rightwards.

Yet from 1981 to 1986 the Labour-run Greater London Council (GLC) challenged the conservative narrative about Britain being undermined by minorities. Instead, it promoted a counter-narrative that the capital – and by implication, the country – needed to end discrimination against minorities and draw on their cultures if it was to become a successful and decent modern society. The GLC’s vibrant and inventive public education and propaganda campaigns are documented in London’s Ours!, a new book by the cultural historian Hazel Atashroo. “Black people do not cause slums,” said one typically direct, dramatically designed poster. “They are forced to live in them.” Many rightwingers were outraged by the GLC’s provocative style and radical goals. In 1985, the office of its ethnic minorities unit was firebombed. In 1986, the GLC was abolished by the Thatcher government. But in the longer term, the GLC won.

Forty years on, Labour often seems to have forgotten how to mount effective campaigns against social conservatism, which Badenoch disingenuously calls “common sense”. Perhaps with a different Labour leader, in an unofficial alliance with other relatively liberal parties, the rightwing counter-revolution could be blocked. It needs to be. A backlash, if left unchallenged, rarely stops.

• Andy Beckett is a Guardian columnist