You can’t doubt the dedication of the crowd packing out this London concert hall on a Tuesday night. For an audience with John McDonnell, they have braved all the muck that a November evening can throw at them. They line up at the end for selfies and book signings. And the very mention of rent controls is greeted with an ovation.

Yet they’re here with good reason. Interviewing the shadow chancellor for this Guardian Live event, it strikes me that what he says and does over the next few weeks matters more for him and for the rest of the country than at any time during his previous 40 years in politics.

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In just a few days, MPs vote on Theresa May’s Brexit deal. Beyond that lies the very real prospect of a general election, or even a full-blown constitutional crisis. And in the background hangs a big question: how radical can any Labour government be? Given the keys to No 11, how far can McDonnell change Britain?

Because, rest assured, that is his aim. Asked about plans for the first 100 days of a Labour government, McDonnell says they must be “transformational”. He promises an immediate increase in the minimum wage, “putting money into people’s pockets”, and a restoration of rights to trade unions. Even without an election, Jeremy Corbyn is already petitioning May to meet senior civil servants about how to turn Labour policies into law. Meanwhile, each shadow frontbencher is going back through the 2017 manifesto and writing out their own department’s “implementation manual”.

What about those much‑debated plans for nationalisation? McDonnell wants water and rail to be the first two industries taken back from the private sector. Energy will take longer, partly because he wants to foster more local energy companies, as is common across much of Europe.

McDonnell has been talking for a only few minutes, and already he has outlined enough work to last any government a decade. Such expansiveness is remarkable for anyone around my age, whose political memory consists in large part of Labour leaders from Neil Kinnock onwards starting with modest, focus-grouped pledges and getting more cautious the closer they get to a poll. Not McDonnell, who now has a plan to recast the British economy in three parts.

First there is what Paul Johnson, head of the Institute for Fiscal Studies, calls “the most radical tax-and-spend plans placed before the electorate by one of the main parties in more than 70 years”. Even they, mind, don’t add up to a reversal of the cuts we’ve seen since 2010. Then Labour proposes re‑engineering the financial system so that it does much more than simply lend money to homebuyers. The biggest and toughest job of all is changing the rules by which markets and businesses are run, such as putting workers on company boards and changing how executive pay is set.

The obstacles to McDonnell’s plans are well laid out in a new book he himself has edited. Called Economics for the Many, this varied anthology of ideas and arguments includes a chapter by Simon Wren-Lewis. The Oxford professor writes: “If Brexit goes ahead and we leave the single market, the UK is likely to remain a depressed economy with low interest rates, and highly vulnerable to negative shocks. As if that were not bad enough, Labour will also face a media that seems incapable of thinking of fiscal policy as anything more than just good housekeeping, and which has not understood how large a mistake austerity was.”

A decline has befallen many institutions that could foster alternative visions of society, from the unions to even the BBC

The word mistake might more aptly be substituted with “crime”, but as a summary this is hard to beat. McDonnell’s response is interesting: it is to signal a big change in Labour’s thinking on Brexit. “I’ve been working through the various scenarios,” says one of the most determined strategists in British politics. First, MPs will chuck out May’s deal, but probably set her the task of tweaking it. But even that, he thinks, will lose a second vote. Throughout, Labour will carry on calling for an immediate general election but McDonnell admits the parliamentary maths means this probably won’t happen. The hard-Brexiteers hate May’s treaty but they know turfing her out will be tantamount to their own career suicide. The DUP might similarly decide to prop her up. At which point, the shadow chancellor says, a people’s vote “might be an option we seize upon”.

The ballot paper for any second referendum would have two choices: May’s deal and remain. In a 180-degree turn from the position he took during Labour’s party conference in September, McDonnell would not include an option for no deal “because of the damage” it would cause the economy. And yes, he would be a remainer. Labour, he says, is a European party.

No wonder Theresa May pounced on these remarks in prime minister’s questions on Wednesday, because this could mark a turning point in the politics of Brexit. After years of what Labour insiders call “constructive ambiguity” on where they stand on leaving the European Union – the hasty call for article 50, the six tests that spell fudge – McDonnell accepts that “we’re running out of road” and that the party will have to jump one way or another. There is still some fantasising about Labour drawing up its own withdrawal agreement, but the sense I take away from Tuesday evening is the shadow chancellor has settled on a plan B – to be seen to exhaust all the options before reaching the destination of a second referendum, which he now describes to the BBC as “inevitable”.

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Two things stand out about Labour’s present thinking on the economy. The first is how many of the problems McDonnell wants to address have been tackled before by Labour governments. Harold Wilson’s government had plans for public investment institutions and wanted to create a department of economic affairs to rival the Treasury. It failed, and not just because George Brown wasn’t up to the job. A quarter of a century ago, Tony Blair latched on to Will Hutton’s The State We’re In, with its proposals to democratise the economy – until he dropped it for the candyfloss of the Third Way.

The civil society that helped previous generations of Labour politicians generate those ideas is much thinner now. The Greater London Council, in which McDonnell began his career in politics, was once an incubator of alternative political ideas. But Margaret Thatcher did for the council and flogged off its base, County Hall. A similar decline and shrinking has befallen many of the other institutions that could foster alternative visions of society, from the unions to even the BBC. All of which means that, if McDonnell and his colleagues are to try to repair the damage that has been done to this country by austerity, and before that by the Thatcherite thugs, they will need more than the Labour party. They will need a full-blown social movement.

• Aditya Chakrabortty is a Guardian columnist