The four British men - who deny all the allegations against them - are being placed on flights from Heathrow to Rome over the coming days.
They are being sent abroad under the controversial European Arrest Warrant (EAW) system, in which crime suspects are extradited at the request of foreign countries without the evidence against them being examined in court.
Colin Dines, 68, a retired judge, his son Andrew, 31, and their colleagues Andrew Neave, 44, and Paul O'Connor, 41, now face 18 months in jail before their case even comes to trial, leaving their families - including a total of nine children, aged one to 10 - with no independent means of support.
The men are expected to be held at Rebibbia prison, on the outskirts of Rome, alongside hardened criminals, including convicted Mafia members.
Mr Neave was placed on an Alitalia flight on Friday evening, with the other three set to follow tomorrow afternoon .
Mr Dines Snr, a former criminal barrister who, during his eight-year career as a judge, sat on courts in London and southern England, said: "We were dragged out of bed at 5am, yet we've never been questioned by the prosecutors in the case. We have never been charged or shown details of the case against us. As a result we have not been able to put up any defence."
The case is the latest of a series of extraditions which have raised questions about the way EAWs - introduced in 2002 by the European Union, following the September 11 terrorist attacks of the previous year - are being used.
The Sunday Telegraph's European Justice on Trial campaign has previously highlighted the apparent injustices of the EAW system, which critics claim is being abused by other countries to target people suspected of relatively minor offences, including many who are innocent and face the prospect of being held in jail for lengthy periods. Parliamentary statistics show that Britain is surrendering 11 people to other countries for every one suspect brought here to face justice under the EAW.
The ordeal of Mr Dines Snr and his three colleagues began when officers from the Serious and Organised Crime Agency (Soca) arrived at their homes early one February morning in 2010, armed with EAWs issued by Italian magistrates investigating a £344 million money laundering operation, allegedly masterminded by the Mafia.
At the same time all their assets were frozen and restraining orders placed on their homes, worth a total of £25 million, preventing their sale.
In January last year Westminster magistrates ruled the men should be extradited after hearing that they were accused by Judge Aldo Morgigni, the Italian investigating magistrate, of being part of a "transnational criminal organisation consisting of more than 10 people" and "complicit in money laundering".
The offences detailed in the EAWs arose out of an investigation by Judge Morgigni into the financial activities of two Italian telecom companies, Telecom Media Sparkle and Fastweb, which has seen the arrests of around 50 suspects.
It is alleged that both firms engaged in "carousel VAT fraud" in Italy, and that the London-based commodity brokerage and telecoms firms companies run by the four men "acted as fictitious clients so that money generated by the fraud was laundered through the companies' accounts".
Mr Dines and his colleagues appealed against the extradition ruling and in February this year appeared before Lord Justice Hooper at the High Court. Although Lord Justice Hooper was a former colleague of Mr Dines Snr and the two men knew each other personally, he did not withdraw himself from the case, as might have been expected.
Indeed, he ruled against the men's appeal, stating there was enough evidence contained in the EAW to warrant further investigation. He wrote in his judgment: "The EAWs set out in detail not only evidence to show that carousel fraud has been committed, but, as importantly, evidence to show that the appellants were involved."
Lord Justice Hooper's ruling opened the way for the men to be extradited, despite a last-minute appeal to the European Court of Human Rights, which was refused.
But Mr Dines and his fellow detainees maintain they have only ever acted honestly.
Speaking to The Sunday Telegraph shortly before his extradition, Mr Dines Snr said: "We have conducted our business dealings with the Italian companies impeccably, but the investigating magistrate looking into them on another matter came across our names on a number of documents. As a result, instead of coming over here and talking to us about it, he has sought a warrant for our arrest.
"We will be thrown into Rome's worst prison for what our Italian lawyers say could be up to six months before being charged and another year of pretrial detention.
"Italy has the worst legal system in Europe, where the standard practice is to threaten and induce detainees in order to obtain admission of guilt in exchange for a reduced sentence. It's worse than plea bargaining, because we are going to be locked up in a foreign country without access to proper legal representation, no bail and our assets frozen."
Mr Dines and his colleagues fear the impact of their arrest will be greatest on their wives and children, who have up till now been allowed to draw only £300 a week per family from their assets. The allowance ceases on extradition, when they will be forced to apply for state benefits, as well as relying on the generosity of their friends.
The families fear that seven of the children may have to removed from their schools as they will no longer be able to afford the fees.
Mr Dines's wife Sarah said: "We don't know when we'll see our men again. It's going to be tremendously difficult for the children, but thankfully we are a close family and we are going to have to come together and help each other get through this. We don't have a choice."
Mr O'Connor, a father-of-four from Richmond, Surrey, who is Mr Dines Snr's son-in-law, added: "We all have clean records. We've never been in trouble before. This is absolutely crazy. Colin has served justice all his life and to send him to jail in this way is outrageous."
The case follows previous controversial uses of European warrants to have Britons extradited.
Earlier this month the trial of two British businessmen, originally extradited to Hungary for five months in 2009 under the EAW system, was delayed yet again.
Michael Turner, 30, from Dorset, and Jason McGoldrick, 39, from Plymouth in Devon, face fraud charges relating to their Budapest-based timeshare company, which collapsed in 2005. Both deny any wrongdoing. They now face waiting until November to learn their fate.
In another case Deborah Dark, a British grandmother who was cleared of drugs charges in France in 1989, found herself detained whenever she tried to travel. Unknown to her, French authorities had won an appeal against her acquittal in 1990. They issued an EAW in 2005, which was only dropped in May 2010.
Mr Dines Snr, who lives in Slapton, Devon, said of the EAW: "The legislation was originally introduced to deal with terror suspects wanted in other countries, yet it is being used to arrest and extradite people who have been accused of committing far lesser offences."
Before being extradited, Mr Dines Snr and his colleagues commissioned an independent expert witness to write a report on the Italian justice system. Professor Stefano Maffei, of Parma University's department of law, was damning in his conclusions.
He wrote: "The current state of Italian criminal justice does not ensure the protection of the fundamental rights of suspects and accused persons under the standards of international law. It is my view that the defendants will suffer serious infringement of their convention rights if extradited and exposed to the Italian criminal justice system."
Speaking about the prospect of spending so many months in a Roman prison Mr Dines Snr said: "Frankly, we are terrified. We will be languishing inside a cell for months on end, through the heat of an Italian summer, in a country with no reputation at all for justice. Our families will be forced to cope without us, our children without their fathers or uncles."
Before preparing to be put on their extradition flights the men issued a last-ditch appeal to Theresa May, the Home Secretary, to intervene on their behalf. But the Home Office said it was unable to comment on the case as it was a matter for the Italian authorities.
Dominic Raab, a Conservative MP who has campaigned against the unfair use of EAWs, said: "This is yet another hit and hope European Arrest Warrant that tears up basic principles of British justice. If the serious allegations of international fraud and money-laundering had any substance, why aren't they being tried in Britain?
"The Italian authorities are extraditing them for investigation not prosecution. Because of the lack of basic safeguards in UK law, they face the endemic incompetence and corruption of the Italian system, and squalid prison conditions you wouldn't wish on your worst enemy. Ultimately, they have been hung out to dry by the British justice system."