British voters’ ruthless rejection of Jeremy Corbyn and his radical socialist project reads like a cautionary tale for leftwing political leaders and parties in the US and Europe. Will Labour’s crushing defeat dim their ardour, or will they double down on revolution?

The general election outcome will embolden Democratic party critics of Bernie Sanders, a 2020 US presidential hopeful whose outlook has often been likened to Corbyn’s. Both men are veteran hard-left campaigners with strong appeal among younger, post-crash voters.

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Sanders is currently running well behind Joe Biden, the main centrist candidate, in most Democratic primary polls, and is vying for second place with another leftwinger, Elizabeth Warren. That has led to speculation about a combined Sanders-Warren leftist “dream ticket”. Yet national surveys of voting intentions show Sanders beating Donald Trump in November next year by an average of 8.4 points. Biden’s equivalent predicted winning margin is 9.8 points. Warren could win, too, the polls suggest. At present, Sanders has no reason to bow out.

Sceptics argue that despite these figures, Sanders cannot win next year. Once voters take a close look at his and Warren’s ideas about universal, NHS-style healthcare provision, business taxes, immigration and workers’ rights, the critics say, they will shy away, as was the case with Corbyn.

Supporters of Sanders and Warren insist the opposite is the case. Corbyn-like, they say they offer voters a chance to change a system that is “rigged” against ordinary working families. Sanders calls this “democratic socialism”. Detractors call it “welfarism”.

Corbyn’s relative success in Britain’s 2017 election was seen as inspirational by some on the American left. Writing in the Nation in April, Robert Borosage was full of optimism about the year ahead. “The coming British and US elections could mark not simply a change of the party in power but the end of the 40-year conservative era and the beginning of a reform era,” Borosage wrote in a commentary headlined: “Bernie Sanders and Jeremy Corbyn might create a Revolution”.

That fantasy is punctured now. Even before Labour’s meltdown, the palpable fear in Democrat circles was that by offering radical reform, rather than simply a safe, mainstream replacement for Trump, the party could forfeit a historic opportunity – and let Trump back in. Labour faced the same dilemma – and missed an open goal.

The grassroots Democratic party, like Labour, has moved further left in recent years. Hillary Clinton’s narrow loss in 2016 was seen on the left as a defeat for discredited notions about where the political centre really lies, and what people really want.

This ideological battle may intensify following the decision of Michael Bloomberg, the billionaire former New York mayor, to enter the race. Biden was quick to wade in on Friday, saying: “Look what happens when the Labour party moves so, so far to the left.”

While Trump would probably relish a one-on-one fight with Sanders or Warren, Republicans worry that Biden and potentially Bloomberg could more easily win over the white, working-class voters on whom the election will hinge and who in Britain defected to the Tories in decisive numbers.

As they reflect on Labour’s failure, European leftwing parties are likely to draw a distinction between Corbyn and his policy platform. Anecdotal evidence suggests personal dislike and distrust of Corbyn on the economy, national security and Brexit were big negative factors.

In contrast, Labour activists insist Corbyn’s ideas about a fairer, more equal society serving “the many not the few”, the ending of austerity, and new funding for health, social care and education were popular on the doorstep. These issues resonate across post-2008 Europe, too.

But while Europe’s social democrats have made a comeback in 2019, finding an unabashedly socialist party that enjoys sole power is a big ask in Europe these days.

Facebook Twitter Pinterest Marine Le Pen will be emboldened by Britain’s rejection of Corbynism. Photograph: Denis Charlet/AFP via Getty Images

Europe’s rightwing populists– Italy’s Matteo Salvini, Marine Le Pen’s National Rally in France, Germany’s AfD, and the ruling parties in Poland and Hungary – will meanwhile enjoy the British left’s electoral debacle. The hard right did not do as well as it hoped in last summer’s EU parliamentary elections. But at national and regional level, it is formidable and gaining.

Germany’s Social Democrats face a particular dilemma. With support at record lows, the party recently picked two leftwingers as joint leaders in a bid to renew itself. Now the SDP must be wondering if it has voted for extinction.

The EU itself is maintaining its usual, lofty neutrality. But centrist leaders such as France’s Emmanuel Macron and Germany’s Angela Merkel will be concerned by the example set by Johnson’s brazenly populist campaign, and what a buoyant rightwing government in London will mean not only for Brexit but for overall future relations.

The stand-out success of the SNP, presaging a possible constitutional clash with Westminster over a second referendum on Scottish independence, is another potential worry for the EU. An independent Scotland seeking instant membership would be an embarrassment. And Brussels certainly does not want another Catalonia.

Crowing and self-congratulation on the right has already started in the US, with suggestions that Johnson has provided a signpost to a Trump second term, in part by persuading long-standing opposition voters to switch sides.

“For the US, the British results are profoundly encouraging,” said Fox News commentator Theodore Bromund. “Britain should now be able to get Brexit done by the new deadline of 31 January. This, in turn, means that Britain and the US will be able to negotiate a free trade area in the near future.”