At last! Labour’s hour has come. Until now, Labour’s voice has been almost unheard in the greatest debate of our time. Jeremy Corbyn has now been obliged to call a vote of no confidence in a government whose policy has crashed in ignominy. No one predicted the monumental, breathtaking scale of this.

Theresa May and her government look set to survive, as Jacob Rees-Mogg dashed out to tell the cameras he would support her against the no-confidence motion. Turkeys – even such a turkey as this Conservative administration – don’t vote for their own demise; they just lead the country to it.

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The chances are that May stumbles on, because there is no one else. Useless though she has been, the constitutional dilemma would be no more soluble under any of the other turkeys lining up in her party to take her place.

The Commons roared its mockery at her belated pledge to reach across the House to consult on what comes next. Too late – two and a half years too late. Had she from day one announced herself prime minister of the whole nation, the defender of the 48% as well as the 52%, she might have forged an agreement to stay as close to the EU as possible. Instead she wasted her time appeasing the extremists, for whom no Brexit can ever be hard enough. She let them feel they ruled the roost – and so they did. And look how low they brought her in return.

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Jeremy Corbyn has no choice now but to steam ahead and at last lead the party he has always promised to obey. Labour members are remainers, overwhelmingly, and they want a vote to decide the country’s fate after these excruciating years of stasis. The majority of people who voted Labour in 2017 support another people’s vote, according the ESRC/YouGov poll and others. Whatever his own views, he has no other course but to do what Tony Benn, his mentor, always argued for – listen to his own party, who go about in T-shirts emblazoned with “Love Corbyn, Hate Brexit”.

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Once the mumbling and doublespeak, the prevarication and the hesitation have at last departed, a remain-supporting Labour frontbench going hell for leather for a referendum will alter the balance of this great debate utterly. The left’s voice has been missing. Whatever pundits say about the Brexit divide cutting across left and right, that’s wrong. Rightwing extreme ideology has motivated the prime movers in this – the wicked, long-term instigators of this national disaster. Labour must fearlessly expose the true nature of the Brexit enterprise throughout all those leave-voting Labour seats.

Never forget, it was Tory voters – the shires, the Tory elderly – who were the backbone of the Brexit vote. Those left-behind Labour towns were a small, if worrying, part of the result. Those places can and must be won back, now that Labour has chosen to no longer be muffled. Roll on a splendid Labour campaign.

• Polly Toynbee is a Guardian columnist