A so-called "European FBI" could save the region hundreds of millions of euros, a long-standing Member of European Parliament (MEP) told CNBC, adding that a "lack of trust" between governments is stopping the idea becoming reality.
Bill Newton-Dunn, a British Liberal Democrat MEP, said the lack of cross-border cooperation between European Union (EU) member states meant criminals could avoid capture.
"Have you ever seen the movie Bonnie and Clyde? They were robbing banks in the 1930s and they got away with it for a long time. The police couldn't cross the frontier to the next state to pursue them. That is how the American FBI got started," Newton-Dunn told CNBC.
He said Europe was in the same position today. "It has open borders and criminals are being very smart and realizing they have a good opportunity to run - all police forces are forbidden to cross a border. It is a very simple thing, if we are going to have open borders then we have to police who can patrol those borders," he said.
The EU's law enforcement agency, Europol, is primarily an intelligence-gathering body, and does not have the power to make arrests.
As such, Newton-Dunn, who was elected to the first European Parliament in 1979, called for a cross-border police force in the EU with wide-ranging powers. He said this European FBI could save the EU "hundreds of millions of euros" in tax revenues lost as a result of criminal activities, such as the sale of counterfeit goods and pharmaceuticals, and VAT fraud.
Exact figures are hard to come by, Newton-Dunn said, but Europol estimates VAT fraud costs EU members around 60 billion euros each year, while cigarette smuggling costs around 10 billion euros annually in lost revenues.
Lack of trust?
However the MEP admitted that a European FBI would face a number of obstacles, mainly due to a "lack of trust" between EU's 28 member states.
"Think of a British policeman. He might say: 'we've got information about some cross border crime, but we don't trust those Italians or Bulgarians.' It falls down time and time again. National governments don't trust each other," Newton-Dunn told CNBC. "[This] is daft because we have to work more effectively to counter crime."
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Last month, British members of parliament voted to pull the U.K. out of 130 European crime and justice measures amid growing concern about the handing over of power to the Europe.
But some have doubts about whether a European version of the FBI would make a difference in fighting crime across the continent.
Pawel Swidlicki, research analyst at the think tank Open Europe, told CNBC: "While it is important for the U.K. to maintain and develop its co-operation with EU partners in the area of crime and policing, there is no reason why the EU institutions need to acquire new powers, a move which would weaken accountability and democratic control."
—By CNBC's Arjun Kharpal: Follow him on Twitter