I spent last week at the Democratic national convention in Philadelphia. In the early hours of the first day of the convention, there was a spectacular thunderstorm with flashes of lightning and crashing thunder. If you were a Bernie Sanders supporter and of a religious bent, you might well have wondered whether it was God herself making clear her displeasure at the prospect of the Democratic party making Hillary Clinton its presidential nominee.

Just one subject was on most people’s lips – the Sanders delegates and how they could be controlled. Many of the people I met were interested in Jeremy Corbyn, who they saw as Britain’s answer to Sanders.

There are many similarities between Corbyn and Sanders. Both, having ploughed their own furrow in progressive politics for over 30 years, have suddenly found themselves at the centre of events. Sanders came within touching distance of getting his party’s nomination and defeating the mighty Clinton machine. Corbyn actually leads his party. But he is embroiled in open warfare with the Westminster elites – political, journalistic and those in the rarefied world of thinktanks.

Both are happy to call themselves socialist. Under New Labour that was the kiss of death for a political career. In the US, it is more dangerous still: in living memory, being accused of being a socialist was enough to get you witch-hunted out of public life.

Both have similar political programmes. Defending or arguing for a health service free at the point of use is vital for both – although Sanders can only dream of a US version of the NHS. Both believe in social justice. They campaign ferociously for the 99% versus the 1%. They battle the power of the big banks and financial institutions. Both believe in a higher minimum wage and investment in infrastructure. Both were early advocates of action on climate change. And it is also worth pointing out that both seem most comfortable when not wearing a tie.

Perhaps the most striking thing, though, is the huge and enthused following of young people they have attracted. Sanders is 74 and Corbyn is 67, but they have mobilised young people in unprecedented numbers, and brought many into party politics who had long rejected it.

It is Sanders’ passionate supporters, young and old, who have proved a challenge to the Democratic party establishment at this convention. They arrived angry and upset because their hero had lost. Many of them despise Clinton, whom they see as everything that is corporate and compromised about the party establishment. They suspected that the primary process had been rigged. Leaked emails seemed to confirm this.

There were demonstrations outside nearly every day and loud booing inside the convention hall every time Clinton’s name was mentioned. Democratic party officials went to extra lengths to keep everyone calm. There were thousands of disgruntled Sanders fans on the convention floor, many of them spoiling for a fight (metaphorically, of course).

Many described themselves as “Bernie or bust” – in other words, they had no intention of voting for Clinton. Some even went in front of TV cameras to say they would rather vote for Donald Trump than Clinton. So Sanders personally texted each of his delegates to entreat them to be calm and respectful.

But as the conference wore on, even the “Bernie or bust” people calmed down. They were encouraged to do so by excellent speeches such as the one by Michelle Obama. The convention has ended and, as the delegates return home, most people believe that even the most passionate Sanders people will vote for Clinton. This is not because they have been persuaded of her merits, but because the prospect of a President Trump is so horrific.

So, with all the parallels between Corbyn and Sanders, will we see members leave in huge numbers if Corbyn loses this summer’s leadership election?

His leadership has had a transformative effect. The Labour party is the biggest it has ever been, with more than 450,000 members. But the idea that the new members are a phantom army who will melt away if only Corbyn can be forced out of the leadership is a delusion put about by his enemies.

Like Sanders, the left insurgency Corbyn is associated with is not about one man or a cult of personality. The insurgency on both sides of the Atlantic is about millions of people realising that “a better way is possible” and wanting to move beyond neoliberalism. That realisation is not going away.

How it plays out in party terms depends on the political actors involved. But it would be a mistake for the party establishment on both sides of the Atlantic to dismiss this insurgency, and think that things can return to how they were.

As the convention drew to a close, the thunderstorms ended, but there was gentle and persistent rain. Sometimes change comes with a thunderclap. But more often it comes with the gentle persistence that the left in both the UK and US will have to show in the coming period.