Just as I was wondering if I had come to the right place, out of the drizzle stepped a familiar figure. “Sorry about the rain,” Jeremy Corbyn told the crowd waiting in a park in Southall, west London, before launching into an eerily familiar speech. For more than a year, I had followed an almost identical politician around the United States, where the climate was more extreme than the London suburbs. From baking-hot Iowa prairies, to the blizzards of New Hampshire, the rise of Bernard Sanders played out on a continental scale. In the made-for-America production, the ageing leftwinger known simply as Bernie rose from nowhere to electrify the 2016 race for the White House. Yet, despite the lower-budget feel of the British version, this movie is getting a remake. Here, too, a leader who was at first ignored, then ridiculed, and now reviled by the establishment, has seen a last-minute surge in the opinion polls that threatens to upset a complacent opponent.

Without wanting to give the plot away, it is important to note that Sanders lost. A mounting wave of support peaked too late for him to overhaul Hillary Clinton for the Democratic nomination and never allowed him to test the polling data that suggested he could have beaten Donald Trump. But the last time an angry white-haired socialist called for political revolution, something nonetheless remarkable happened. Against all the odds, Sanders found millions more Americans were enthusiastic about radical social change than even he imagined was possible. Ideas that once seemed absurd by the old standards of Washington politics set the country alight.

In one way, Labour’s leader has already gone further than the failed candidate for the Democratic nomination by winning his party’s support twice. Despite narrowing opinion polls, political pundits are not alone in thinking that a national victory is still all but inconceivable. But a lesson of the tumultuous US election is that nothing is predictable in our febrile modern politics, and nothing may be the same again.

The widespread support revealed by Sanders for policies such as wealth redistribution, trade protection, free universities and universal healthcare continues to confound expectations. The implosion of Trump’s presidency, and the centrist wing of the Democratic party, has left Sanders by some measures the most popular politician in America. Though rightwing critics in Britain also try to paint Corbyn as outside the political mainstream, the whole political spectrum is arguably shifting to the left, with even the Tories copying Labour economic policies.

Students in South Carolina show their support for Bernie Sanders in the 2016 Democratic primary. Photograph: Richard Ellis/EPA

Corbyn’s election performance next Thursday is perhaps therefore only part of the story of where the Labour party goes next. This is more than just about trying to emulate successful Sanders techniques of political organising, online campaigning and public speaking. It is about whether the British left can overcome the suspicion of working-class voters to harness the same mood of populist revolt that led to victories for Brexit and Trump – but turn it in a progressive direction.

Sanders, perhaps the only politician in the world to have done this at scale, arrives in Britain on Thursday for sold-out speaking engagements in Brighton, Brixton, Oxford and the Hay-on-Wye festival, a long way from the rustbelt battlegrounds of either country. With Labour hoping for flattering comparisons and possible endorsement, I set back out on a different campaign trail, this time with team Corbyn, to compare notes.

Tracking the Labour leader down proved a surprise early challenge. Anxious to avoid a hostile press pack, the party does little to promote his public events, especially among national newspapers. Local journalists and television crews are tipped off, as are activists. Otherwise, it can be like trying to find a secret rave – where the curious are reduced to quizzing fellow travellers at the railway station. Like playing a socialist version of Where’s Wally?, as someone else joked while trying to find the big red bus before our next rendezvous.

The 45th event of Labour’s truncated election campaign turned out to be at Peterborough United football ground. But whereas Sanders filled 14,000-seat stadiums like this for nearly a year, Corbyn spoke only to invited party members in an upstairs conference suite containing barely 1% of the ground’s capacity. The nearby town centre, where the Tories are defending a majority of less than 2,000, was left untouched.

Even a local activist, a retired electronics worker who says he waited all his life for a true socialist to lead the party, was made to wait in the foyer for an hour longer because his email registration had failed to make it on to the list at the door. The handful of journalists who breached the cordon sanitaire were ordered not to ask questions, perhaps so as to make time for probing inquiries from the audience such as: “Is it true that this June we will see the end of [Theresa] May?”

Sanders also had a hate/hate relationship with the US political media, but pulling up to a rally, in a country largely without public transport, there was usually just one uncertainty: would there be a parking space left? The vast audiences – a mixture of young idealists and older voters who found living the American dream to be an increasing nightmare – were passionate but rarely stage-managed. No teleprompters or notes were needed. Hearing it nearly 100 times did not change the underlying message or its power to shock. In fact, the raspier his indignant Brooklyn voice became, the more authentic it sounded.

Corbyn supporters show their faith at a speech in West Kirby, Merseyside, in May. Photograph: Paul Ellis/AFP/Getty Images

It was a strategy once said to have worked well in different circumstances for Ronald Reagan: relentless repetition of a simple story about what the country had become and what it could still be if the audience believed enough. Sanders’ speeches in Britain this week still carry the same slogan as his US presidential campaign – “A Future To Believe In”. Corbyn’s equivalent, “For the many, not the few”, strikes a jarring, perhaps more divisive tone. Though he never made it past the Democratic primary, Sanders used a party election to try to talk to a nation; Corbyn can feel as if he is still using a national election to talk to the party.

Though the secrecy has at times fostered a word-of-mouth buzz, most excitingly at recent rallies in Hebden Bridge and Leeds, the one stadium crowd Corbyn has addressed, at Tranmere Rovers, was primarily there to see a music festival.

Perhaps the excitement and novelty peaked during Labour’s first leadership battle. “Jez we can” came before “Feel the Bern” – the slogan that the Sanders campaign used to effectively to rally online enthusiasm. Video taken of early Corbyn rallies in places such as Liverpool while he was campaigning for the leadership matches the euphoria of late-stage Sanders in Chicago or California.

But there are signs on the ground of the “Jez we can” excitement returning. Those with experience of the insurgent campaigns on both sides of the Atlantic see similarities in how they are able to respond more authentically than nervous frontrunners such as Hillary Clinton or Theresa May. “When your opposition is trying to carry a vase across a room, it opens the door for so much fiery activism and devoted door-knocking,” says Simon Bracey-Lane, a British volunteer organiser for the Sanders campaign in Iowa, who is now canvassing against the Conservatives.

The mood on the doorstep has changed dramatically since Corbyn’s poll surge, he says, and the buzz is “100%” like that around Sanders. “In the US, I met people who had lost faith in politics but were being reminded of what a good man looks like, and I think that is what Jeremy Corbyn has managed to capture,” adds Bracey-Lane. “That has the effect of galvanising people to go above and beyond. This is exactly what we saw with Bernie and that is what we are seeing with Jeremy Corbyn.”

These events also share a homespun enthusiasm, attracting hand-painted campaign posters that defy the sceptical national media. The only occasions I witnessed supporters threaten to deliberately obscure the cameras of unfavourable television networks were at Corbyn and Sanders rallies; never those of Donald Trump.

Bernie Sanders celebrates his victory in the race for Congress in Vermont in 1990. Photograph: Rob Swanson/AP

As Labour senses it may be losing its pariah status, Corbyn appears to be seeking a more inclusive message. “This is our chance to deliver history to the people of this country,” he told the Peterborough faithful. “Elections are, yes, about knocking on doors and talking to voters, but they are also about framing the debate. I have been very clear that this is a national debate.” An awkward interview with Andrew Neil on Friday was defused by the almost Obama-like promise of national “hope”.

Yet the new left on both sides of the Atlantic eschews anything too polished or media-friendly. Both Corbyn and Sanders revel in their status as grumpy old men. Both children of the counterculture, famously pictured being arrested at civil rights protests in their youth, they have been accused of dressing scruffily but rarely seem to care. Both beyond normal retirement age, but with wives 20 years younger, they come from liberal bastions such as Islington and Brooklyn that are usually viewed with suspicion in the rest of the country, yet they remain outsiders among metropolitan elites too.

Both struggle most with issues of identity. Sanders’ achilles heel was his poor showing among black voters, a mainstay of Democrats, particularly in the American south. Corbyn struggles with the equally crucial constituency of white voters in the north of England. Both have been accused of failing to recognise that people are bound together by more than just economic and class interests. Their success in appealing to students and young voters suggests they have at least latched on instead to the looming divide between generations. “Our manifesto is very different,” Corbyn tells the youthful crowd in Southall. “Not a ladder for the few but a staircase that all children can go up.”

Much of their stump speeches are interchangable: “The richest five families in Britain own the equivalent of the total wealth of 20% of the entire population,” says Corbyn. “We live in a grotesquely unequal society and it’s getting worse.”

“Income and wealth inequality is the great moral issue of our time, the great economic issue of our time and the great political issue of our time,” says Sanders.

“I’m angry,” explains the Labour leader, often, but politely. There is no need for such running commentary with Sanders, who was constantly hoarse from railing at the “billionaire class”.

Corbyn has more of a sense of humour. “For the Tories, Surrey is the hardest word,” he quips. “You’re supposed to laugh at that.” But the Labour leader is more easily riled too, choosing to take offence at a union rep who suggests he should come to Peterborough more often.

While Labour wants a £10-an-hour minimum wage, Sanders calls for $15 (£12) – an almost identical goal once adjusted for relative national incomes. Both want banks to pay for ambitious infrastructure programmes.

Jeremy Corbyn is arrested at an Anti-Apartheid Group picket of South Africa House in London, 1984. Photograph: Rob Scott

Where they do differ on policy, it mainly reflects the varying political starting points of Britain and the US. Sanders wants to create an NHS-style health insurance system; Labour wants to protect it. “I was with family in the US over Christmas with a group of young people,” recalled Corbyn in Peterborough. “And they all ended up talking about health insurance. That conversation never happens here.”

On foreign affairs, both have been accused of being soft on terrorism but appear to be winning the argument that Anglo-US military adventurism has been hugely counterproductive. Where Corbyn is attacked for being close to the IRA, the Democrat was threatened with attack adverts from those who claimed he was a communist sympathiser.

The biggest difference, however, is that Sanders rarely allowed his patriotism to be questioned or become a distraction from his core political message. While Corbyn appeared to alienate traditional working-class voters by refusing to sing the national anthem, Sanders actively courted the non-metropolitan blue-collar vote with policies on gun rights that risked opprobrium from liberal voters. He may have been a 74-year-old Jewish New Yorker, but he was right at home in the depressed manufacturing towns that were to prove decisive in the 2016 US election.

Sanders was also surrounded by some of the smartest young minds in political campaigning. The digital team that propelled #FeeltheBern to the forefront of social media also helped attract 100,000 on-the-ground volunteers who spoke to 75 million voters in the run-up to the Democratic primaries. A record-breaking fundraising drive helped garner enough advertising dollars to blunt the hostile media onslaught.

Whether it would have been enough to blunt an even more aggressive blitz from Donald Trump and the Republicans will remain one of the great unknowns of US politics. Although Sanders would have struggled like Clinton in diverse areas such as Florida, it is hard to imagine him suffering the catastrophic collapse in Democrat support in the five rustbelt states of Ohio, Michigan, Wisconsin, Pennsylvania and Iowa that ultimately cost her the election.

Reading too much across into a British context can be a futile exercise, but the biggest lesson perhaps is how quickly accepted political wisdom can be made to look foolish in the face of a populist surge. Opinion polls have been much derided on both sides of the Atlantic, but in the Democratic primary they mainly just proved to be backward-looking rather than prophetic. In Sanders’ case, they tracked a wave of national recognition that peaked too late to make a difference. Yet he was still to win 23 primary elections – 22 more than anyone expected outside his fanatical home state of Vermont. He came from 60 percentage points behind in national opinion polls to briefly draw level with Clinton, and secured 46% of pledged delegates at the national convention. In Michigan, Clinton was an average of 21 points ahead in the polls before she lost to Sanders. He also won despite being 28 points behind in Colorado and 34 points behind in Minnesota.

Labour supporters who have seen May’s lead over Corbyn cut from similar numbers down to as little as five points will be wondering if an even more fairytale ending is still possible in Britain.