There is no sugarcoating the fact that on the basis of last week’s elections, Reform UK is now the largest party in British politics, if only by vote share. It is still a long way from ever winning power at Westminster, but we don’t need to look far to see whether a Reform government would try to make good on its various threats – because Reform is our local version of an international wave of populist rightwing nationalism.

This loosely connected movement has declared its hostility to the checks and balances that prevent democracy from becoming a tyranny of the majority, or even of those with only a plurality of support. It can be chaotic and destructive, like Nigel Farage’s beloved Donald Trump, or slow and grinding like the recently departed Hungarian government of Viktor Orbán. But we can make a reasonable guess as to what life under a Reform government might look like – and I suspect it’s something that neither you nor I would welcome.

Yet Reform’s success is not inevitable. With hundreds more seats in English local government and a sizeable presence in Scotland and Wales, Reform has an unprecedented opportunity to convince people it is a genuine contender for power. But this masks a number of weaknesses, not least the fact that its share of the vote dipped compared with last year’s local elections. Reform benefited this time from a more fragmented political landscape overall, but it’s possible its support has hit a ceiling, at least for the moment.

A more fundamental weakness lies in the very essence of Reform as a rightwing populist party. This style of politics surfs on a multitude of resentments, promising people that their sense of pride and belonging can be restored by redrawing the borders of national identity more narrowly and punishing those who stand in its way. Reform’s sinister promise to place immigration detention centres in areas that vote Green is a case in point. This is what gives Reform its edge, but it is a mixed blessing. Ostentatious cruelty won’t actually improve the lives of its supporters, so a party that does business this way must either race to outdo itself with even more extreme pronouncements, or back down and lose credibility.

That is a huge potential weak spot, particularly as Reform is now under more scrutiny than ever. It’s especially true in English local government, where Reform has actual decision-making power, a system that has been so starved of resources it is a poisoned chalice for any party. It’s even more difficult for one whose representatives are largely untested and in some cases unfit for office, and which has spent several years claiming there is a magic money tree to be found by cutting “wasteful” spending on diversity initiatives. (Spoiler: there isn’t, as suggested by the difficulties faced by existing Reform councils.)

There are at least three ways this weakness might be exploited. The first is through a revived centre right. That might seem counterintuitive to a left-leaning reader, but in western Europe the centre right once provided a durable barrier to radical rightwing challengers. It was most successful in the postwar period when those challengers tended to be parties seeking to revive fascism – in most places there was a taboo against collaborating with the people who had brought much of the world to ruin in the mid-20th century. But a glimmer of this persists in Germany and France, for instance.

Britain’s Conservatives were once skilled at containing rightwing discontent – for example, by drawing a clear line against rhetoric they deemed unacceptable, as Edward Heath did when he sacked Enoch Powell as a shadow minister in 1968 for his racist “rivers of blood” speech. Could the Conservatives do something similar again? It’s unlikely anytime soon. By deciding to compete on Reform’s territory, rather than take a stand against reactionary politics, Kemi Badenoch has taken what was once the UK’s most successful election-winning machine to new lows.

The problem goes deeper than poor leadership. As the sociologist Phil Burton-Cartledge argues in a recent book, the Tories’ traditional base has decayed, partly because recent Conservative governments presided over a period of stagnating wages and rising housing costs that have reduced the supply of affluent homeowners, the bedrock of their support. The party’s membership today, which is older and more socially conservative than the general population, is not inclined to elect or select leaders and candidates who are capable of rebuilding the party’s mass appeal.

If so, then the challenge will have to come from elsewhere. The latest polls suggest a large potential bloc of left-leaning and socially liberal parties, ranging across Labour, the Greens, the Liberal Democrats, the Scottish National party and Plaid Cymru. It is fragmented, but could at the very least be mobilised as a “stop Reform” coalition as a short-term electoral tactic. In places where no one party has a majority – which includes many English councils as well as the Scottish and Welsh parliaments – politicians will need to show they can work together productively.

The deciding factor here is Labour, which once dominated this bloc but is now a wounded beast – too big to ignore, but paralysed by its current leadership; unable to adapt to a changed electoral reality and lashing out at the people it needs to work with. In April, the home secretary, Shabana Mahmood, told a heckler who accused her of “out-Reforming Reform” with her hardline immigration policies to “fuck right off”. Labour’s current problem is that too many people took her advice on 7 May. The problem for other parties is that not enough people did. That means difficult conversations about how to cooperate.

The third and final hope is you. We cannot wait for other people to come along and fix this on our behalf. Reform’s success so far results from the failure of mainstream politics: a failure by successive governments to ensure that wealth and power are spread around the country fairly, and that we have the resources to care for one another when we are vulnerable; and a failure by those same governments to challenge the toxic resentment on which Reform thrives.

If we want to stop Reform then we need to speak up – to hold its figureheads accountable for their rhetoric and their decisions; to challenge those elsewhere in Westminster and the media who pander to Reform’s agenda; to demand politicians across the board serve our interests and not only those of the powerful, or of a narrow section of our communities. Large, national protests against racism – like March’s Together Alliance demonstration in London – are important symbolism and good for morale.

But they only work if the energy they attract feeds back into the places where we actually live. Last week, many people were elected to office around Britain on the back of some very big promises. We can hold them to account by keeping informed about their decisions and complaining or campaigning when they fall short. This goes for politicians across the board, but it’s particularly important in Reform-controlled areas where the party’s effort to attract two very different groups of voters at once – low tax, low-regulation Thatcherites and a more collectivist-minded group who are nostalgic for well-funded social democracy - is likely to run into trouble.

Rightwing nationalists like Reform understand very well that nations are made, not born. “A nation without a culture is not a nation at all. It’s just an economic zone, a shopping mall with a flag waiting to be exploited,” Reform’s home affairs spokesperson, Zia Yusuf, said earlier this year. He has half a point. But Reform just wants a bigger flag and a higher fence around the shopping mall: it is on the rest of us to show that our culture is already more expansive, stronger and welcoming than this withered vision of identity could ever encompass.

• Daniel Trilling is the author of If We Tolerate This: How the British Establishment Made the Far Right Respectable