What is taking place in the Labour party is a democratic explosion unprecedented in British political history. Last week more than 168,000 registered to vote in Labour’s leadership election – on one day. About 400,000 people have applied to join Labour as members or supporters since May, tripling the size of the party to more than 600,000.

Overwhelmingly, it’s the response to one candidate standing for the Labour leadership: the veteran backbench campaigner Jeremy Corbyn. When Tony Blair became Labour leader in 1994 he promised to recruit 1 million members, but never got much beyond 400,000. Corbyn has sailed past him in weeks.

Not only that, but the leftwinger is now runaway favourite to win the contest. In the most recent poll, Corbyn was scoring 53% on first preferences, 32 points ahead of his nearest challenger. And 32% of the public say they would be more likely to back Labour under Corbyn, seven points more than any other candidate.

After years of handwringing about declining participation in party politics, you might imagine the political class would be delighted at this grassroots surge. Not a bit of it. The political and media establishment has linked arms to resist it. This is one of Her Majesty’s parties of government, after all. The idea of it falling into the care of someone outside the boundaries of political acceptability is unthinkable.

So one New Labour grandee after another – from Tony Blair to David Miliband – have taken time out from their lucrative post-ministerial careers to brand Corbyn as the road to electoral oblivion. Far from welcoming this vast influx, they want the party declared full up.

Allowing supporters to sign up US or French primary-style, a change welcomed last year by Blair as “something I should have done myself”, is now damned as a perilous gateway to political entryism. So there have been attempts to close down the contest, weed out undesirables, or even convince Corbyn’s three rivals to withdraw to halt the election.

But the more New Labour’s college of cardinals brands the Corbyn surge a self-indulgent spasm, the more it exposes official politics as a closed system whose rules of what is credible and electable are set by the powers that be rather than by voters or party members.

The Corbyn phenomenon is a movement that nobody predicted or got up behind the scenes. With its echoes of the Scottish referendum campaign and European leftwing populist movements, it’s a backlash against grotesquely narrowed political choices and a punitive austerity imposed to pay the costs of the 2008 crash.

The Jeremy Corbyn effect: John Harris charts the rise of the Labour leadership contender Guardian

You only have to go to one of the campaign’s huge rallies to understand that the idea this is the product of political or union manipulation is laughable – and that his supporters don’t only want a different kind of Labour leader: they want to change the political system.

Meanwhile, the claim that the other leadership candidates – steeped as they are in the triangulating “pro-business” politics of the 1990s – can offer a winning electoral alternative to Corbyn’s commitment to what are in fact mostly mainstream public views, looks increasingly implausible.

Andy Burnham has now broken ranks with the “anyone but Corbyn” bloc, while the Blairites are swinging behind the studiedly New Labour Yvette Cooper. But their spat looks like a battle for second place. The most recent polling found 61% of eligible women voters, against 48% of men, were backing Corbyn – which is perhaps not so surprising, given the disproportionate impact of austerity on women.

Corbyn’s opponents insist that he’s a throwback offering “old solutions”. That seems to be based mainly on his commitment to public ownership of rail and energy – which is not only supported by large majorities of the public but also reflects a growing trend towards new forms of social ownership across Europe, especially in Germany.

As each denunciation has failed to dent Corbyn’s lead, they have become more poisonous

The real objection is that Corbyn represents a break with City-backed austerity and a powerful commitment to public investment. Add to that his opposition to Trident renewal and endless British warmaking, and the challenge he represents to the establishment consensus is obvious enough.

So as each denunciation has failed to dent Corbyn’s lead, they have become more poisonous. The latest target is his support for dialogue with Hamas and Hezbollah, combined with an attempt to smear him by association with antisemitism. As Blair himself has met Hamas’s leader, Khaled Mish’al, four times since April, it’s a bizarre line of attack.

But the desperation is a measure of what is at stake. The main charge is that Corbynmania is an unrepresentative flash flood, that Labour lost the election because it was too leftwing, and that a Corbyn-led Labour party is unelectable.

That any Labour leader will face a mountain to climb is not in doubt. But May’s results, which saw Labour leak support in all directions, don’t bear out such claims at all. There isn’t in any case only one possible coalition of voters that could beat the Tories in five years’ time. And the idea that any of Corbyn’s rivals stands a better chance of winning back support in Scotland, from disaffected working-class and middle-income voters, Ukip or the Greens is hard to credit.

It’s possible, of course, that the relentless attacks will tip the vote against Corbyn after all. But if not, he will face an even more ferocious onslaught thereafter. That will come not only from the Conservatives and the media, but from sections of the Labour establishment that can be expected to launch a parliamentary campaign to undermine and unseat him.

But Corbyn will have an unprecedented democratic mandate if he wins, backed by a movement of hundreds of thousands. And not only is he committed to creating a leadership of “all the talents”, he also plans to open up Labour’s long-dormant internal democracy. Corbyn makes a point on the stump of emphasising that his policy ideas are currently only “proposals” and “suggestions”.

By any reckoning, this is a high-wire act. Even if he wins, he could be ousted – or “rugby-tackled”, as Blair put it – further down the road. But for now the Corbyn movement offers the chance of a break with a disastrous austerity regime – and for a real democratic opening.