There is a widespread view in far-left circles that the European Union ranks among the world’s foremost neoliberal institutions, along with the US Congress and the White House under Donald Trump.

Even Remain supporters can be heard at Labour party meetings saying things such as: “The EU is a neoliberal construct, but we should be changing it from the inside, not walking away.”

Without this gnawing sense that Brussels is run by an elite, one that is hell-bent on taking Europe on a path to privatisation, all but the most ardent sovereignty campaigners would probably want to stay inside the EU. The MPs John Mann and Caroline Flint wouldn’t be under pressure from their constituency members and unions such as Unite and the RMT to back a Brexit deal. Jeremy Corbyn and his advisers might even get on board the People’s Vote bus, ditching the halfhearted stance they have adopted up to now.

There is still time to take a less blinkered view as we near the end of the article 50 negotiation period. Not much time, granted. But without a dispassionate reassessment of the EU, it is likely that a majority of MPs, mostly Tory with Mann and Flint in tow, will vote for Theresa May’s revised deal when it is put before parliament either this week or next. It’s that or the UK crashes out, which also remains a possibility.

If we accept the definition of neoliberal as the pursuit of free markets, low taxes and privatisation at the expense of state regulation, public welfare support and state-run services, then the most recent example of such behaviour is the EU demand that Greece takes this road to redemption.

According to the leftwing Brexit, or Lexit, viewpoint, the Germans took over as the driving force behind Brussels’ reform agenda in the wake of the financial crisis and the Greeks were one of their main victims.

Its a simple argument. Unfortunately, that is its only attraction. As with most disputes, it is more complicated and there is wrong on both sides. For a country such as Greece to claim that its overly generous state benefits should be protected by its neighbours, which in the main do not enjoy such benefits, was always a stretch.

From the standpoint of most European leaders, not just the Germans, it wasn’t the EU that forced Greece to almost bankrupt itself funding the 2004 Athens Olympics. It wasn’t the EU that forced Greece to build up its military spending to become one of the highest in Nato. In fact, in 2015, only six other Nato countries had military personnel costs higher than Greece’s.

Linked to this tale is the austerity the Greeks must suffer for many more years. It’s true the EU can block domestic budgets that overstep debt rules. However, it hasn’t prevented the Syriza government from tackling corrupt businesses, taxing wealthy households and overhauling a public sector that is lubricated by backhanders.

Jacob Rees-Mogg: It’s easy to understand why rightwing Brexiters want to escape the EU and its demands for basic rights. Photograph: Leon Neal/Getty Images

Another recent example of Brussels’ neoliberal tendencies is the plan to force governments to offer up their rail networks to competitive tender. This is viewed as the thin end of a large wedge that would see the EU push through the privatisations of most utilities, much as the UK has already done and which the Lexiters dream of reversing.

In his book on Europe’s privatisation experiments, Private Island, James Meek shows how the sale of state assets to private firms relies for its “success” on driving down costs, usually with steep wage cuts and weak terms and conditions of employment to the fore.

However, the way privatisations have been carried out in the Netherlands, Italy and the UK has been under domestic regulations, not the diktat of Brussels. The generosity of minimum wages, the strength of union laws and enforcement of employment regulations above the minimums set by Brussels are governed by member states.

In the case of rail privatisation, a closer look shows that the EU rules are flexible and allow state-owned businesses to run trains. State-owned businesses can also operate the underlying rail network, as happens in the UK, though operation of trains and network must be separated.

Critics on the left say Brussels has been captured by lobbyists for multinational companies. They say this without acknowledging that Brussels is blocking monopoly mergers and the exploits of the tech companies with more rigour than any other jurisdiction.

It’s easy to understand why Boris Johnson and Jacob Rees-Mogg want to escape the EU and its demands for basic rights, but for those on the left who want to achieve better workers’ terms, to follow their lead only gives rightwing Brexiters the destructive tools they crave.