Just a month ago, in his crusade to take his flock back to basics and deliver it from the clutches of Mammon, Pope Francis said the Church "must go forward... with a heart of poverty, not a heart of investment or of a businessman".

St Peter, he noted, "did not have a bank account". As we learnt a few weeks later, though, the senior Vatican official Monsignor Nunzio "Don 500" Scarano certainly did – at least two of them, which, prosecutors say, he used to smuggle €20m (£17.3m) into Italy from Switzerland, and to launder money used to buy a €1.7m luxury flat in Salerno.

Don 500 – so named because of his tendency to dish money around in the form of €500 notes, the criminal's favourite denomination – can't be dismissed as an isolated case. Two years ago there was the affair of Evaristo "Don Bancomat" Biasini, an official working for the Congregation of the Missionaries of the Precious Blood, who was accused of shady financial dealings in the construction sector.

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Most damaging for the Vatican is the role that its own bank, the IOR (Institute for Religious Works), may have played in these affairs. In the case of Mgr Scarano, investigators are in no doubt he used his two IOR accounts like overseas slush funds. Records show that on one occasion last year Mgr Scarano withdrew €560,000 from an IOR account in a single transaction. He is currently in the Regina Coeli prison, awaiting trial. On Friday the Vatican announced it had frozen his assets and warned that other people may be caught up in the investigation.

Aware of the IOR's scandal-struck reputation, Pope Francis hired a new president for the institution, Baron Ernst von Freyberg, in May. The German industrialist immediately made himself a hostage to fortune, however, by declaring that the IOR was a "well-managed and clean financial institution" whose reputation was paying the price for past scandals.

Last week finance police and magistrates, led by Giuseppe Pignatone, released a report on their 30-month investigation into the IOR. The document said that high demand for recycling cash, together with the lack of checks and controls by the IOR and the Italian financial institutions it had dealings with, made the Vatican's bank a money-laundering hot spot. The two men in charge of the IOR's daily operations, the bank director Paolo Cipriani and his deputy, Massimo Tulli, immediately quit after six years in their jobs.

Within hours Baron von Freyberg released a new statement: "It is clear today that we need new leadership to increase the pace of this transformation process." Pope Francis appeared to share this view, appointing a five-person commission to examine how the Vatican's finances are run. But those hoping for a truly independent assessment must have been disappointed by the line-up.

Instead of a breath of fresh air, there are only Vatican insiders. The most detached of the five appears to be Mary Glendon, 74, a former US ambassador to the Holy See who heads the Pontifical Academy for Social Sciences. But like the other five commission members she has an IOR bank account.

Another commission member is Mgr Peter Wells, 50, a high-ranking figure in the church's governing body, the Curia, who, like Ms Glendon, has personal connections to fellow American Carl Anderson. Mr Anderson is a member of the IOR's board of directors and head of the wealthy Knights of Columbus, which has been described as the "Catholic masons".

Vatican-watchers say this doesn't mean that Pope Francis is averse to cleaning out the stables – or doing something even more radical. "I think Francis's natural inclination is to shut the damn thing down," said Robert Mickens, the veteran Vatican correspondent of The Tablet. But like other experts he believes Pope Francis will be feeling the full force of vested interests in the Holy City.

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Some at the Vatican will be quick to remind Pope Francis that the IOR gives the Holy See tens of millions of euros a year that help it pay the electricity bills and overseas trips – and keep it in the black. The Italian press has speculated that the notion of closing the IOR may have produced the threat of fresh Vatileaks-style disclosures from those who want to maintain the status quo.

An idea of who these people might be is emerging from Mgr "Don 500" Scarano himself. Under interrogation by Rome magistrates, and apparently intent on securing house arrest in his 700-square-metre apartment lined with art by Giorgio de Chirico and Marc Chagall, rather than time in a jail cell, Mgr Scarano is shedding a light on the murky workings of the other key financial institution in the Vatican, Apsa (Administration of the Patrimony of the Apostolic See), which administers the Holy City's finances – and whose key figures benefit from IOR accounts.

One name keeps coming up: that of Paolo Mennini, who heads the division of Apsa that looks after the patrimony of the Holy See. He has been called the Pope's merchant banker. Investigators are particularly interested in cash flows totalling €230m that occurred between 2009 and 2011 from Apsa accounts to London banks. As Rome's Il Messaggero newspaper noted, these probes have extra piquancy given that in this period Apsa declared income of only €22m and paid just €3m in tax.A look at the history and connections of the Mennini family produces a list of facts and incidents that would have Dan Brown wringing his hands in envy. Paolo Mennini's brother Antonio, who has served as the Vatican's ambassador to Britain since December 2010, was the priest sent to hear the final confession of the kidnapped prime minister Aldo Moro before his execution by the Red Brigades in 1978. Vatican influence has ensured he's never had to testify at state hearings concerning Moro's abduction and murder. More pertinent perhaps, is the career of their father. Luigi Mennini, who died in 1997, was managing director of the IOR in the period following the collapse of the Banco Ambrosiano, in which the IOR was the major shareholder. This was the scandal that involved the killing of "God's Banker" Roberto Calvi in London, and the suspicion that the IOR was linked to the mafia and money-laundering.

On 31 May this year, shortly after his appointment, IOR president von Freyberg announced on Vatican Radio that he had a dream: "My dream is that our reputation is such that people don't think of us any more, when they think about the Vatican, but that they listen to what the Pope says."

But so it appears, did one of his recent predecessors, the respected financier Ettore Gotti Tedeschi, who was removed for his trouble. Officially, Mr Gotti Tedeschi was himself investigated in 2010 regarding a money-laundering scandal and later stepped down after a no-confidence vote by the bank's directors.

But Mr Gotti Tedeschi didn't go quietly. He insisted he got the boot because he'd ruffled too many feathers in his attempts to clean up the IOR by introducing greater transparency and targeting non-religious holders of IOR bank accounts. His claims were backed by last week's report by magistrates and finance police.

With this in mind, Pope Francis might have second thoughts regarding the advice he is now seeking. One of the voices critical of Mr Gotti Tedeschi was the IOR board director, Carl Anderson of the Knights of Columbus, whose influence could now be felt on the special committee Pope Francis has convened.

If he is serious about tackling financial sleaze, Pope Francis may be better off listening to his instincts – and take an axe rather than a broom to his tainted bank. As Mr Mickens noted: "After all, what's to stop priests and nuns using ordinary bank accounts like the rest of us?"

God's bankers

For an institution whose main role is looking after the money of priests and nuns, the IOR has had a remarkable number of scandals in its 71-year history.

The most notorious concerned the collapse in 1982 of the Banco Ambrosiano, in which the IOR was a major shareholder. The Vatican paid around £150m to compensate Ambrosiano's account holders – without admitting any wrongdoing. The then head of the bank, Archbishop Paul Marcinkus, was indicted but claimed diplomatic immunity as a high-ranking Vatican official. But events became much murkier when Ambrosiano's chairman, Roberto Calvi, known as God's Banker, was found hanging from Blackfriars Bridge, London in 1982. Calvi's death was eventually classed as murder, following two inquests and an independent investigation. Prosecutors said he was killed for stealing mob money.

Many of the scandals have involved "papal gentlemen" – Italian businessmen, industrialists and aristocrats who assist at papal ceremonies and so are entitled to IOR accounts. Francesco La Motta, formerly high up in the secret service, has been a papal gentleman since 2007. He was arrested last month and accused of illegally transferring €10m of state funds out of Italy. Another, Angelo Balducci, was arrested in 2010 on corruption charges linked to building contracts.

Last July EU inspectors said the Vatican bank had failed on seven counts to clean up its act. The report said the IOR had made progress, but it would remain outside the "white list" of countries that abide by global norms on combating money laundering, financing terrorism and tax evasion. The report "strongly recommended" the bank be "independently supervised by a prudential supervisor in the near future".