The statement said Dawes` gang trafficked cocaine from South America to Europe and heroin from Turkey and Afghanistan to Britain.
It said some 50 people linked to the group have been arrested in different countries in recent years.
The statement said three Dawes gang members were among 30 arrested in 2013 after French police seized 1.3 metric tons (1.43 tons) of cocaine in 32 suitcases on an Air France flight from Venezuela.
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