Is the Greek crisis a reason for Britain to quit the European Union? Several Guardian columnists – Owen Jones, George Monbiot and Suzanne Moore – have argued that it is. But this is mistaken. Their conclusions are based on a distorted view of what is happening in Greece.

Rightwing British Eurosceptics have for long salivated at the prospect that Greece might be expelled from the euro. Although they are shedding crocodile tears at the plight of the Greek people, their motive is to milk the crisis to advance their domestic political agenda: Britain’s exit from the EU.

The new phenomenon is the surge in leftwing Euroscepticism. This is based on the perception that Greece has been bullied into accepting austerity by other eurozone countries, led by Germany. Progressives have swallowed undiluted the propaganda pushed out by Greece’s radical left Syriza government: that the EU is an organisation that rides roughshod over the people’s democratic wishes because it is hellbent on imposing a bankrupt neoliberal economic ideology.

If this impression takes root, it could have severe consequences. It could undermine the left’s support for Britain’s EU membership. Given that the Conservative party is also split on the issue, there would be a serious risk that the country might vote no in the coming referendum. David Cameron has been careless in calling such a vote and blithely assuming he can rely on Labour backing yes solidly. But being able to pin the blame after the fact on the prime minister will be little comfort for pro-European progressives if the result has been Britain quitting the EU.

There is much that is correct in the left’s narrative on Greece. For example, the euro was badly designed, with a bias towards deflation. What’s more, Greece should not have joined the currency, as its economy wasn’t fit enough to endure the straitjacket of a single monetary policy.

What is progressive about people not paying taxes and retiring under the age of 50?

Once the crisis hit, Athens should have been allowed to default on its debt (much of which was then held by foreign banks) rather than borrowing extra money from fellow eurozone countries. It should also not have been required to implement so much debilitating and self-defeating austerity.

But there is also much that is wrong in the left’s narrative. It doesn’t mention that Greece had many deep-seated problems that pre-dated the creditor-imposed austerity: rampant tax evasion, an epidemic of early retirement, a bloated public sector and a private sector carved up by special interests. These problems need to be corrected before Greece can thrive. It doesn’t help to label these necessary reforms as neoliberal. What is progressive about people not paying taxes and retiring under the age of 50?

The left narrative also ignores the fact that the creditors’ tough love policy has worked in four other countries: Spain, Ireland, Portugal and Cyprus. Things are far from perfect, but all these economies are growing again. Greece was growing too, until the last conservative government stopped implementing the bailout programme a year ago. Six months’ rule by Alexis Tsipras then turned a mild downturn into a full-blown recession.

Syriza, of course, blames the creditors for the recession, arguing that they ran a deliberate policy of choking the economy in order to bring the government to heel. But, while the eurozone has not played the role of an angel, the main culprit is the prime minister himself.

Tsipras made wild pre-election promises that he couldn’t deliver; he chose a confrontational firebrand, Yanis Varoufakis, as his finance minister; and he failed to develop either a credible plan for cutting a deal with his creditors or a proper plan B in case he was unable to do so. Britain’s progressives, however much they sympathise with the Greek people, should not align themselves with such incompetence.

But didn’t the eurozone, and especially Germany, trample on the democratically expressed wishes of the people? Well, not really. There’s no theory of democracy under which one country’s politicians must do what another country’s people want. German leaders are elected to represent their people, not the Greeks. We would get pretty angry if Cameron started doing what, say, the Poles demand rather than what we want.

David Cameron has been careless in calling such a vote and blithely assuming he can rely on Labour backing yes solidly

Of course, countries should try to help one another – especially close allies who share the same currency. But it’s not true that the eurozone hasn’t shown any solidarity. Although much of the money was used to bail out foreign banks, a big chunk went to rescue Greek banks and another dollop went to plug Athens’ budget deficit. What’s more, the creditors have already given Greece some debt relief by agreeing to low interest rates and allowing the country a long time to repay its borrowings.

Eurozone countries haven’t been nearly as helpful to Greece as they could have. But what on earth has this to do with our own membership of the EU? We are not in the euro and, if we pulled out of the EU, that wouldn’t help the Greeks one iota.

What we would be doing is sacrificing our own interests. We would be settling for second-class access to Europe’s single market, which accounts for half our trade. We would also be diminishing our ability to address a range of challenges – such as global warming, organised crime, terrorism and Russian militarism – that cross borders. That wouldn’t be good for Britain. Nor, for that matter, would it be good for Greece.