If it is true that failure makes a great teacher, the Liberal Democrats must know a lot about British politics. Currently they are learning about Brexit by failing to capitalise on the votes of millions of remainers, despite being England’s most pro-European mainstream party. In 2016 support for EU membership was 48%, yet the Lib Dems struggle to reach double digits in opinion polls.

That reflects another failure: at a time when Jeremy Corbyn has taken Labour radically to the left, and Theresa May’s agenda is dictated by the fanatical right, there must be room for a party of mainstream moderation. But Vince Cable’s tribe, gathered in Brighton this week, has not expanded into that space. They look peripheral even when they’re parked in the middle of the road.

The electoral system makes life hard for small parties, but that explains only how an appealing challenger would struggle to achieve an electoral breakthrough. It doesn’t explain why the Lib Dems don’t even appeal. And there are signs of appetite for alternatives. One recent poll found more than a third of respondents saying they felt unrepresented by Labour or Tories. On the question of a preferred candidate to be prime minister, “don’t know” beats May and Corbyn.

The Lib Dems look peripheral even when parked in the middle of the road

When voters say they crave something different, they often mean something new. The Lib Dems had their insurgent moment in the 2010 election when, briefly, Nick Clegg looked like the mould-breaking candidate. That romance didn’t survive complicity with Tory government.

To witness the Conservatives’ recent descent into ideological mania is to give some retrospective credit to the Lib Dems as a restraining influence, but that doesn’t extend to an enduring image of the party as some kind of stabilising agent in British politics, which is how Clegg hoped they would emerge from coalition. It was an intellectual as well as a technocratic ambition. He saw liberalism as his party’s unique heritage and a quality that Labour and Tories were equally prone to neglect. There are indeed authoritarian impulses of left and right that manifest themselves when either side is allowed to monopolise power.

In that context, the absence of a Lib Dem revival raises an interesting question. Does their malaise say anything meaningful about the health of liberalism itself? And by extension does a defence of liberal democracy require renewal of the party that named itself after the idea? Cable thinks it does. Well, he would, wouldn’t he, but there is a way to plot the Lib Dem rise and fall on a graph of bigger trends in British politics: the party was ascendant in the era of New Labour, when there was a high level of consensus around third-way economics and a generational flourishing of social-liberal values. The Tories, then cantankerous and reactionary, seemed doomed to atrophy on the cultural margin. They only regained power under David Cameron by tilting towards liberalism – a shift conceived originally as a question of tonal “modernisation”, and then enacted institutionally by reliance on Clegg’s MPs for a parliamentary majority.

But the coalition hollowed out the political centre. Austerity fired the left’s appetite for socialism. The right felt betrayed by Cameron’s arrogant metropolitan style – his support for gay marriage; his dismissal of Ukip as “fruitcakes, loonies and closet racists”. By 2015 to 2016, Corbynism had captured Labour and Brexit-propelled nationalism had captured the Tories.

To project the tumultuous events of recent years through a Lib Dem lens flatters the party’s significance, but it illuminates a problem for a wider tribe that feels politically adrift right now. They see the collapse of the liberal centre as a moral calamity: the ascendency of foul populism. But to insurgent forces of left and right, the centrist lament is just the nostalgia of a deposed, discredited elite. Liberals themselves don’t seem sure whether their business is restoration of the old order or rebellion against a new one.

That dilemma is incarnate in the figure of Sir Vince. He has proposed reforms to open his party to loosely affiliated supporters – “a movement of moderates” – to counteract extreme polarisation of British politics. But his style radiates lethargic ancien régime self-pity. In fairness, Cable has recognised his incipient obsolescence and promised to stand down next year. His reforms hint also at recognition that the party’s brand might be beyond redemption. Renewal of the Lib Dems as a mass movement feels less probable than Lib Dem submersion into a wider force evolving from the vibrant ecosystem of grassroots anti-Brexit campaigns. In parliament, dissident Labour MPs are confident the Lib Dems will fold into any breakaway faction they might form.

The Lib Dems can heal Britain's economic divide – here's how | Vince Cable Read more

The mustering of a new force looks inevitable but not imminent. Partly that is because the menace that anxious liberals decry is still hypothetical for much of the country. Brexit looms, but hasn’t actually happened yet. The spectre of hard-left authoritarianism is a subject mostly discussed in the context of obscure internal Labour party machinations. Meanwhile, the concerns that have driven people away from the political centre are less abstract – immigration, wage stagnation, cuts to public services, feelings of neglect by political elites over many years. The liberal lament can sound ethereal compared to those grievances.

That doesn’t mean that liberalism is secure. The peril of British politics being captured by its wilder fringes is real. The appetite for something neither Labour nor Tory is surely real too. But the rubble where the old centre ground collapsed doesn’t necessarily indicate the best spot to erect something new. Also, if there is the need for a mass movement to defend liberal democracy, it is a task far too important to leave in the incapable hands of the Liberal Democrats.

• Rafael Behr is a Guardian columnist