Democracy has never been the European Union's strongest suit. It's an institution where the unelected and the barely accountable have always called the shots – and electorates are routinely made to vote again if they get the answer wrong in a referendum. So perhaps it's no surprise that as soon as it became clear the Greeks would be given another say on the austerity programme that has already driven their country into 1930s-style depression, the threats and bullying began in earnest.

The entire European establishment has now lined up to scare Greeks off giving another majority to anti-austerity parties, as they did in explosive elections earlier this month. Europe's revolt against austerity has to be contained. Democratic niceties about not interfering in other countries' elections have been ditched. If Greeks vote for parties such as the radical left Syriza – now leading in most opinion polls – they will be voting to leave the euro, Europe's political elite has warned.

"To remain in the euro," the unelected EU commission president José Manuel Barroso declared, "Greece must respect its commitments". By commitments, he meant the package of pulverising privatisations, tax rises and cuts in jobs, pay and services demanded by the EU and IMF in exchange for loans which cannot be repaid and are reducing the country to beggary. Knowing most Greeks both reject death-spiral austerity and want to stay in the euro, Europe's political class is ratcheting up the fear of forced exit meltdown.

Most preposterous has been the British prime minister David Cameron lecturing Greeks on their responsibilities from outside the eurozone. "You can either vote to stay in the euro, with all the commitments you've made," he declared, "or you're effectively voting to leave". Fellow Tory minister Ken Clarke warned the Greeks of "serious consequences" if they voted for "cranky extremists". This from a government that demands growth from Europe while driving its own economy into a double-dip recession with homegrown austerity.

Meanwhile, the Irish are getting similar treatment, as the country's elites try to scare voters into backing the EU's permanent austerity treaty in a referendum later this month. Crucial to the campaign has been the threat that Ireland will be denied future emergency bailout funds for its own shrinking economy if the treaty is rejected. So far, that has kept the yes campaign ahead, even though Sinn Féin has mirrored the European trend by doubling its support to more than 20% on the back of opposition to the country's failed austerity programme.

But in both cases, the threats are phoney. The legal basis of the treaty clause the Irish government is claiming would cut off future bailout funds is strongly contested and the prospect unrealistic. And Greeks are not voting on whether to stay in or leave the euro next month. They are voting on whether to continue to reject a shock therapy programme that even those demanding its implementation know can only drive Greece deeper into debt and destitution.

There is now a strong likelihood that the country will end up leaving the euro, whichever way it turns – and that may well offer Greece the most realistic chance of eventual recovery. But it's not what parties such as Syriza are demanding. Instead, its leader Alexis Tsipras has been in Paris and Berlin this week calling for a halt to Greece's debt repayments, and negotiations with Europe's leaders on a new deal.

The stronger the vote for anti-austerity parties, the better the chance that those negotiations could produce more than cosmetic results. That's because the threat of a disorderly Greek default – which could still take place inside the euro – has the potential to trigger a cascade of bank runs and knock-on crises across the eurozone whose impact could dwarf the Lehmans crash of 2008.

Greece is, after all, only the state furthest down the road of collapse. The threat to crippled Spain could already be on a much larger scale. Across the eurozone, the banking system is once again tipping towards breakdown, as self-defeating austerity deepens the crisis.

As one EU commissioner told me yesterday, "this austerity union is simply not sustainable". Eurozone leaders' attempt to solve the crisis by "internal devaluation" – cutting wages and services across the southern periphery to restore competitiveness – was a "complete disaster", he said, that would deliver mass poverty and migration to the north.

But despite hopes that France's new president François Hollande, now backed by Barack Obama, could shift Europe towards jobs and growth, the concessions potentially on offer from Germany's Angela Merkel are not remotely on the scale necessary to overcome the growing crisis. That would need a commitment to fullblown eurobond lending to underpin state debts, a Marshall plan-style programme of fiscal transfers and investment in weaker eurozone states, along with recapitalisation and public takeover of European banks.

But Germany's leaders show no sign of being prepared to foot the bill for the costs of a currency union that has benefited German capital above all but now threatens, like the gold standard in the early 20th century, to bring Europe's economy to its knees.

But the eurozone's implosion isn't only the result of a cockeyed, one-size-fits-all currency structure that was always going to buckle and fracture under pressure. It's also the product of the wider crisis of neoliberal capitalism that first erupted in the banking system five years ago and has since wreaked havoc on public finances, jobs, services and living standards throughout the western world.

Asked who they held responsible for the Greek crisis at the weekend, 50% of Britons polled rightly blamed the banks, 22% Brussels – and only 4% the Greek people. But the eurozone breakdown is also the product of a generation of EU treaty-enforced privatisation, market deregulation and corporate liberalisation that paved the way for the crisis across Europe, including in Britain.

It's that inbuilt neoliberal dimension of the EU, central to debates in mainland Europe, that has been missing from the growing political pressure for a referendum on EU membership in Britain – but has played a central role in this crisis. Across the continent, whether in or out of the eurozone, the need for a break with a failed economic model could not be more pressing.

Twitter@SeumasMilne