No doubt, in the coming days, many more column inches will be dedicated to Julian Assange's battle against extradition to Sweden. His case, however, is the tip of the iceberg. In 2009 more than 4,000 people were extradited under Europe's fast-track extradition system, 700 from the UK alone.

This kind of EU co-operation may help in the fight against crime but the benefits of a streamlined system should be weighed against the heavy toll taken upon an individual when surrendered to another state.

A few days ago, four of Fair Trials International's clients spoke in parliament about their personal extradition ordeals. These examples clearly demonstrate that the European arrest warrant is not operating "efficiently and in the interests of justice".

Frank Symeou explained how his 21-year-old son, Andrew, spent a year in horrendous prison conditions in Greece. Eighteen months after he was extradited he is still waiting for the trial to start.

Edmond Arapi described his 12-month battle against extradition to Italy where, with no notice whatsoever, he had been sentenced to 16 years for murder. Ultimately, Italian judges were persuaded that Arapi could not possibly have committed the crime and the wrong man had been convicted. He had spent weeks in custody, torn from his young family.

Similar examples of injustice are happening all over Europe. In the Netherlands, for example, a political storm is brewing over the case of Cor Disselkoen, a 65-year-old man who is due to be extradited to Poland (a country that issues about one-third of European arrest warrants).

Disselkoen suffers from a severe heart condition and is the primary carer for his terminally ill son. He faces charges for an alleged fraud dating back to the mid-1990s, allegations he strenuously denies. Given the notoriously bad conditions in Polish prisons there is a fear that, if extradited, he would not survive the ordeal.

At the heart of the problem with the European arrest warrant is the inability or unwillingness of Europe's judges to prevent injustice. The standard retort to arguments against extradition is that we must co-operate with our European neighbours, we must trust them to do the right thing. We do, of course, need an effective system of extradition in Europe: we cannot allow people to evade justice by crossing Europe's open borders. Given the grave human consequences of extradition, the current blind faith approach to justice is not acceptable.

On occasion, judicial frustration at this no-questions-asked system overflows. Last year, before concluding that he could not stop Garry Mann's extradition to Portugal, Lord Justice Moses spoke of the court's "inability … to rectify what appears to be a serious injustice to Mr Mann".

"I cannot believe anybody wants this man to go and do two years in an Albufeira jail. It is just an embarrassment for everybody, this whole case, and it ought to disappear," he said. Garry is in Portugal serving a two-year sentence.

The scales finally seem to be falling from the eyes of those responsible for the warrant. A review is under way in the UK to examine its operation and the European justice commissioner, Viviane Reding, has recently acknowledged "there is considerable room for improvement in the operation of the arrest warrant system".

The challenge is to fix the system by building in much-needed safeguards against misuse and injustice. Fair Trials International has given the UK's extradition review panel suggestions on how this could be achieved. Until it is, many more people will suffer an unjustified extradition ordeal and public confidence in the European arrest warrant will continue to ebb away.

Jago Russell is chief executive of Fair Trials International