“We are the grown-ups now.” So said several speakers. In the grotesque political playground of Brexit Britain, Labour has indeed become the nation’s adults, the sensibles, the party least likely to wreck the country’s future. How short a time ago Jeremy Corbyn and John McDonnell were regarded as delinquent adolescents who had never grown out of the 1970s. They may be the masters soon.

What a transformation. Remember how early in the general election campaign they fell 11 points behind in dismal local council results? Whatever Labour leaders say sourly now to those of us who feared the worst, waiting for that exit poll in June they too were braced for heavy losses, never expecting a crushing humiliation for Theresa May.

Cynics say Labour is lucky: who could fail to shine in contrast to the most chaotic and shameless government in living memory, wrestling each other to death even as they drag the country over a precipice of their own devising?

Those of us who doubted them feared that winning elections was not their aim

This mutinous Tory crew, who loathe one another with tigerish ferocity, are responsible for an economy in a dire state. Paul Johnson, the head of the Institute for Fiscal Studies, the great referee of truth in a fake-fact world, warned a Resolution Foundation meeting here at Labour’s conference that everyone was underestimating the situation’s severity. Labour says living standards haven’t fallen so far since Napoleonic times; Johnson says not since the 1750s, with productivity the worst ever recorded. We are, he says, in frighteningly uncharted territory. He adds the Office for Budget Responsibility’s warning that Brexit will worsen public finances: making trade more expensive “is guaranteed to reduce living standards further”.

Strictly non-partisan, Johnson criticises many Labour spending promises – but these are the economic facts the country faces as GDP per capita falls further behind the rest of the EU, national and personal debt rises and our credit rating tumbles. Surely any opposition would soar after years of such mismanagement, even one led by two people recently regarded as leftovers of Labour’s looniest era?

But success changes all, and the sudden prospect of power has transformed Corbyn, McDonnell and their team. Those of us who doubted them feared that winning elections was not their aim: they would prefer to ride their ideological hobby horses regardless of what the public wanted. But now they’ve tasted electoral nectar, they want more.

Emily Thornberry, effusive about Corbyn, said he had done so well because “nothing is stronger, nothing on earth than a person of principle … whose unshakeable values will carry him to Downing Street”. Well, up to a point. What’s encouraging is how his team has embraced pragmatism. The brilliant manifesto that overnight shifted Labour’s fortunes mid-election was pure retail politics: for large sums they enticed calculated demographics – the young with tuition fees, the old with the unmerited triple lock and, less noticed, a pledge to never raise the pension age, however how long we live. They promised no tax rises except for the top 5% and corporations. But only crumbs for the poor: an ironist might say that the slogan “for the many not the few” meant for the majority of voters, not the few who struggle with least.

Gordon Brown and Tony Blair did great good to the poorest, with tax credits, Sure Starts and much more - but they too did it by stealth, fearing that redistribution was no election winner. Now Corbyn and McDonnell do likewise, listening to the public mood, being careful not to alienate too many, fudging the tricky issues. Here is a party in pursuit of power, making compromises, offering electoral blandishments, doing (almost) whatever it takes to keep Conservatives out of power because a Labour government will always improve the lot of those in most need. Graciously, McDonnell’s speech praised the good done by every Labour government: Attlee, Wilson, and yes, Blair and Brown too.

Who would have thought they would be so Wilsonian? But he is their model for blurring their Brexit dilemma. Corbyn is a free movement, pro-migration man, but he stifles that: he is anti-single market and more or less stifles that too. The vast majority of Labour members and two-thirds of Labour voters are appalled by Brexit – but pragmatism warns the party against losing northern Brexit seats. Keir Starmer has led them cleverly along a wobbly tightrope towards near-as-damn-it-but-not-quite-yet staying in the single market and customs union, without affronting northern Brexiters. Timing is everything, even if it infuriates passionate anti-Brexiters who marched and rallied in Brighton.

Forget Corbyn’s pitch about giving the party back to the members: an old fashioned top-down stitch-up denied delegates the chance to commit the party to free movement and the single market. Corbyn, that serial rebel, has learned that discipline is essential for any party serious about power. For a reminder, he need only glance across at how indiscipline is wrecking May’s party.

Momentum is merging into mainstream Labour: if grabbing the party’s levers of power obsesses a few old-style plotters, the people here, so swollen in numbers, are the same decent people you find in any local party, the people who keep local public services running against the odds, who run the credit unions, food banks and citizens advice bureaus, as well as knocking on doors and running raffles. There are vanishingly few zombie Derek Hattons risen from the Militant grave. If these ordinary members now have more say on policy, the party looks safe enough in their hands.

Leading figures from Labour’s many eras are here, some bereft, some bewildered by new, unfamiliar shadow ministers. Like the rings on a tree trunk you can find the circles of old old Labour, old New Labour, overtaken Brownites and once-dashing Milibandists, some of yesterday’s younger people perplexed at the rise of an older generation. But the best have recovered from the shock, finding Corbyn’s Labour not such an alien beast after all, embracing the new radicalism and plans they would like to have dared to make themselves – taking back control of utilities and PFIs.

No one in their right mind would predict anything. Corbyn could be prime minister next year, in five years or never. The scale of the Brexit calamity and its political fallout is unknowable. But Labour looks more credible by the day, its senior team more impressive: one reminder here is the roster of excellent Labour mayors and leaders running the country’s best councils, while Kensington and Chelsea stands as the Tory’s sorry emblem. The hard truth is that Labour’s fate hangs less on its own talents than on the unpredictable fate and Euro-irrationality of the chaotic party in power.

• Polly Toynbee is a Guardian columnist