One of the downsides of Brexit is that the EU arrest warrant would no longer apply and fugitives from justice, including suspected terrorists, might be free from extradition.
The EU arrest warrant was introduced in 2003 and in the 1990s it was quite common for British criminals to get on a plane to Spain and hide out on what was known by British newspapers as the "Costa del Crime" without fear of extradition.
Cyprus, in particular Turkish-occupied northern Cyprus, was another frequent bolthole for British criminals.
There are also fears that, with the EU arrest warrant no longer applying in Britain, European fugitives could simply jump on a plane to Ireland, drive over the border into Ulster and find themselves safe from extradition to France, Germany or wherever.
Dr. Anna Bradshaw, a lawyer and member of the Law Society's EU Committee, gave evidence to Parliament in March about how Brexit might impact on not just the EU arrest warrant, but also cooperation between British and other law enforcement agencies.
"People focus on the EU arrest warrant because it is so visible, but there are so many other ways in which we cooperate with other EU countries and all of these are jeopardized by Brexit.
"The EU arrest warrant has had a lot of criticism, but by and large it has been an overwhelmingly successful exercise," Dr. Bradshaw told Sputnik.
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"Before it was introduced EU countries would have extradited between themselves, but the framework was different and some countries had national laws which prevented the extradition of their own nationals, which the EU arrest warrant superseded.
"One of the main advantages has been the introduction of time limits. An EU arrest warrant must now be dealt with within 60 days of arrest. Outside the EU there are no time limits and that impacts on the wider cost of extradition proceedings and the cost of keeping that person in custody," she told Sputnik.
Prior to the EU arrest warrant many jurisdictions would have applied the "double criminality" rule, which meant that someone would not be extradited unless the same offense existed in the country they were being extradited from.
But under the European Arrest Warrant framework, the double criminality rule does not apply in respect of 32 categories of offense, provided the requesting member state punishes those offenses by a prison sentence of a maximum of at least three years.
During the referendum campaign many Brexit campaigners dubbed the Remain campaign "Project Fear" because they had raised concerns about matters such as the EU arrest warrant.
The Leave campaign claimed Britain would still be able to extradite people and have them extradited even if they were not in the EU.
But Dr Bradshaw said: "It's dangerous to presume that there will be the same motivation for other EU member states to continue the same level of cooperation as they have in the past and it will be difficult for the UK to continue without signing up to the European Court.
"After Brexit, when UK authorities make extradition requests, they may find them being treated as less of a priority than requests from other EU member states," she told Sputnik.
In an age when terrorists, especially those sympathizing with Daesh, often cross EU borders before and after committing atrocities, information exchange between law enforcement could be threatened by Brexit.
"The EU has multiple information exchanges in place and they are in the process of consolidating these, but no one really knows how Britain will be able to continue in these exchanges post-Brexit," Dr Bradshaw said.
Already Brexit has had a chilling effect on police cooperation.
Britain recently missed the deadline to sign up to the European Investigation Order, a mechanism which was designed to do for mutual legal assistance what the EU arrest warrant did for extradition.
"The UK had signed up to it, but I suspect it has been put on ice by Brexit," Dr. Bradshaw told Sputnik.