The idea of modern banking was born in Siena in 1624, when the Medici Grand Duke decided to guarantee accounts held at Monte dei Paschi, the world’s oldest bank, with the proceeds of pasture he held in the Maremma in south-western Tuscany.

Nearly 400 years later, the principle established by the Tuscan ruler – that account holders and investors are protected by the state – lies at the heart of a crisis at Monte dei Paschi di Siena (MPS) that is worrying financial markets around the world.

The country’s third-largest lender has already been bailed out twice in modern Italian history but is likely to need a third multibillion-euro intervention by the Italian government – a move that would need Brussels to break new rules designed to prevent such taxpayer bailouts after the 2008 global financial crisis.

So the question of who will pay for the inevitable rescue of MPS, whose share value has fallen 80% over the past year, has yet to be answered.

Three weeks after the news that Britain has voted to leave the European Union shocked the markets, a debate over the fate of MPS and the economic and political repercussions of inaction is raging from Rome to Brussels and Paris to Berlin.

The welfare of thousands of Italian households is at stake, as well as the political fortune of Italy’s prime minister, Matteo Renzi, who is facing the toughest political challenge of his career. It is also testing Italy’s credibility among foreign investors.

“There is no way they will let the bank go and create a systemic effect,” said Wolfango Piccoli, co-president of Teneo Intelligence. “The mechanics are still unclear but there will be a third bailout of Monte dei Paschi.”

The bank’s financial problems are neither new nor surprising. According to the IMF, Italian banks have €360bn (£300bn) of non-performing loans – loans that are likely to turn into bad debts – mostly taken out by small Italian businesses battered by years of recession. Italy returned to growth in 2015 but the improvements are only modest and this week the IMF said the country’s GDP was not likely to return to pre-crisis levels until the mid-2020s.

Unlike the US, Spanish and Irish financial crises, the Italian banking crisis is not the result of a speculative property bubble. While other issues have exacerbated the turmoil at Monte dei Paschi’s – including a poorly judged €9bn acquisition – the primary reason the bank is in trouble is because it doled out billions of euros in loans to small businesses at a time when the scale of the recession facing Italy was gravely underestimated.

From 2007 to 2013, Italy lost about a quarter of its industrial production and tens of thousands of companies collapsed. In 2013 more than 150 shops closed every day. Construction and home sales slumped and none of the sectors has recovered fast enough.

“These are all problems that are well known and have existed for years. The government – not just this one but the previous one – should have acted earlier,” said Vincenzo Scarpetta, an analyst at Open Europe.

Now the collapse of Monte dei Paschi’s shares, coupled with concern brought on by Brexit and fears that the Siena bank will fail a vital bank stress test on 29 July, has forced Italy’s hand: the banks need a bailout of about €45bn – a sum that most experts argue cannot be raised from investors.

During years of inaction by successive Italian governments, the country’s banks missed a critical window of opportunity. They are now subject to European banking regulations that would force the bank’s bondholders to take a significant hit before the state can inject funds. About a third of those bondholders are ordinary Italians.

Renzi’s government has already had a bitter taste of how badly the crisis could go if Italian pensioners were wiped out by the new rules. Last November the prime minister passed a decree in which four regional banks were saved. While depositors and senior bondholders were protected in the deal, thousands of junior bondholders were wiped out, leading one pensioner to commit suicide and a political backlash against Renzi.

But Brussels has so far shown little interest in the domestic economic risks and the potential for political backlash.

Last month Angela Merkel, the German chancellor, said that the EU would not veer from the new rules. Renzi retorted that he was in no mood to be “given a lesson by the schoolteacher”.

Earlier this week Jeroen Dijsselbloem, the Dutch finance minister and the head of Eurogroup, the informal grouping of EU’s finance ministers, downplayed the extent of Italy’s banking woes. “There have always been and will always be bankers who say: ‘We need more public money to recapitalise our banks’ and I will resist that very strongly because it is, again and again, hitting the taxpayer,” he said.

Dijsselbloem was partly responding to Deutsche Bank’s David Folkerts-Landau, who has argued that Brussels needs a €150bn bailout to begin a major recapitalisation of European banks. Analysts in Italy have raised questions about the huge UniCredit and local banks Rimini and Cesena.

Renzi holds an important card in this fight. His Democratic party is the only major political party in Italy that has shown unwavering support for the euro and the EU. His biggest rival, the populist Five Star Movement, is gaining traction following two big wins in local elections in Rome and Turin and could displace Renzi if the prime minister fails to win a critical referendum in the autumn on his sweeping constitutional reforms. He has sworn to resign if the referendum fails.

While the constitutional reforms and the banking crisis are not directly linked, Brussels is keenly aware that support for any Renzi initiative will be guided by voters’ view of the economy.

“If Italians lose faith in the banking sector it is a huge problem because going after the banks has always been a big card of the Five Star Movement,” said Piccoli.

“If something goes badly wrong with the banks – like a run – it would potentially bring down Renzi’s government because [it has] been saying the banks are solid.”