The UK will have to rely on pre-EU agreements, rather than the European Arrest Warrant (EAW), says the Law Society.
Some EU states have repealed the 1957 European Extradition Convention, leaving Brit taxpayers footing legal battles to boot out foreign criminals.
Britain risks becoming a “safe haven” for dangerous crooks and thugs from the Continent, the society warned.
And UK efforts to snare those suspected of committing crimes in Britain then fleeing the country, such as the Salisbury poisoners, would be hampered.
Law Society chief Christina Blacklaws said: “The British people may not be forgiving if the UK becomes a safe haven for criminals from the EU27.
“Even where the 1957 European Extradition Convention is still in place, the process is lengthy, costly and taxpayers will end up footing the bill.”
She added: “Switzerland still uses it, so the evidence of the system’s defects is there for all to see. Under the convention, extradition arrangements with the EU would again become a political decision, with the involvement of the Home Office.
“It would also create problems with Ireland, as that’s one of the countries which has repealed legislation – they would have to amend their domestic law, as would a string of other EU27 countries, which might not be a priority for them in the wake of an ill-tempered exit.”
A number of EU states including Germany, France, the Czech Republic, Holland, Slovenia and Slovakia would have to change their constitutions to allow extraditions of citizens to a non-EU country.