Jeremy Corbyn is not the first leader of the Labour party to have form as a Eurosceptic. Hugh Gaitskell was so fearful of the drive for European political union that he warned about Britain ending a thousand years of history as an independent state. Clement Attlee was no big fan of what was then called the common market either.

But this was all a long time ago. Under a succession of leaders starting with Neil Kinnock, Labour warmed to Europe. In the 1980s, with Thatcherism rampant at home, the party saw Brussels as providing protection from free-market zealotry. In the 1990s, under Tony Blair, the feeling was that globalisation had made the nation state redundant.

Even so, a small number of Labour MPs remained unreconciled. They pointed out that Labour’s love affair with Europe began just as Europe’s economic performance started to deteriorate. They opposed the Maastricht treaty that paved the way for the single currency on the grounds that it would create an undemocratic central bank with deflationary tendencies.

Corbyn was one member of this band. John McDonnell, now the shadow chancellor, was another. Unlike the majority of their parliamentary colleagues and most trade union leaders, they never bought the idea that being a progressive meant being positive about Europe. They saw nothing especially progressive about mass unemployment, the impact of the common agricultural policy on the developing world, the Transatlantic Trade and Investment Partnership, or the bias towards austerity ingrained in the stability and growth pact. Rather, they saw neoliberalism being hardwired into the European project. As indeed it was.

None of this really mattered until Corbyn became Labour leader two years ago. But since 2015 the maverick outsiders have become the maverick insiders. What’s more, the shambolic state of the Conservatives means that Corbyn and McDonnell could soon be neighbours in Downing Street and responsible for Brexit. Parliamentary arithmetic and the determination of the Tories to avoid another election at all costs makes this unlikely, but these are strange and unpredictable times. What Corbyn and McDonnell think about Europe now counts in a way that it didn’t before.

Leavers have come up with no solutions for sorting out the country’s long-term economic problems

Both men campaigned for remain in the referendum, albeit not with great gusto. Labour’s 2017 manifesto pledged to honour the result of the referendum. The leadership has come down hard on MPs who tabled amendments to the Queen’s speech demanding that Britain stay in the single market. All of which is significant. Corbyn and McDonnell are smart enough to understand the risks of Brexit, but they also see it as an opportunity to push through their own economic agenda. Which is why they are exploring the freedom Brexit would provide for public ownership, lower rates of VAT to help those on the lowest incomes, state aid to support sunrise industries, and fair trade agreements with developing countries.

Remainers on the left would argue that there is no need to leave the EU for this to happen, but they are wrong about that for two reasons. The first is that a radical socialist programme that included a different approach to state aid, state ownership, public procurement and managed trade would be deemed illegal under European law. The second is that without Brexit, the impetus for change would quickly dissipate.

So what, say remainers. The status quo is better than Brexit, the baleful consequences of which are already clear from the slowdown in the economy and warnings from banks and transnational firms that they will move at least some of their operations out of the UK unless they get the sort of deal they want.

But the left needs to be very careful about running with the idea that business should be able to veto decisions made by the electorate. If Labour had won the recent election, Corbyn would have had a mandate for extensive nationalisation, ending austerity and higher taxation on companies and the well-off. Big business would certainly have cut up rough about all that. There would have been warnings from the Confederation of British Industry about its members moving thousands of jobs out of the country. Would those calling for a second EU referendum be calling for another general election so voters could think again about supporting such a dangerously radical policy? Probably not.

Nor, given that Britain has been through the decade from hell, is the idea of a return to the status quo especially attractive. The four freedoms of the single market have made it easier for companies to move money, goods, services and people around the EU, but workers have not benefited. There has been virtually no growth in UK per-capita incomes since the start of the financial crisis in 2007, something that has not happened outside wartime in the modern age.

Britain is a low-wage economy with a chronic balance of payments problem. Repeated bouts of de-industrialisation mean there has not been a surplus on manufactured goods since the early 1980s. Growth has become ever more dependent on consumers’ appetite for debt, and the willingness of the Bank of England to make servicing that borrowing as cheap as possible. The UK’s poorer regions are 20 years behind the south-east in terms of living standards.

These problems are not new. They were there long before David Cameron decided to hold an EU referendum, and they will be there regardless of whether Brexit happens or not. Remainers on the left have spent the past year bemoaning the referendum result and have expended a great deal of intellectual energy thinking up ways to hold a second referendum or, failing that, to come up with a Brexit that in effect returns Britain to where it was on 22 June 2016.

They have quite legitimately asked leavers to explain what Britain will look like after leaving the EU. But they have come up with no solutions themselves for sorting out the country’s long-term economic problems. The assumption seems to be that all will be well provided Britain’s supply chains are protected by continued membership of the single market, and the City retains its role as Europe’s premier financial centre. This is sheer fantasy. If membership of the single market were a panacea, Britain would not have the weakest investment record of any G7 country. Nor would it be running such a big trade deficit.

Capitalism’s ability to see off its rivals has always been based on the notion that it will make people better off, even if some people benefit more than others. But that pledge has been broken. Historically, profound political change only happens at times of crisis. Without the Great Depression and the second world war, there would have been no Labour landslide in 1945. Without the crisis of the mid-1970s, there would have been no Thatcherism. Without the crash, there would have been no Brexit – and Corbyn would still be a backbencher.

As it is, Labour is now led by somebody who spent years in the political wilderness with a simple message: that there was something inherently rotten about modern capitalism; that there were radical solutions to that malaise; and that Europe was part of the problem, rather than part of the solution.